Petitioner Ricky Fulcher appeals the district court’s denial of his 28 U.S.C. § 2254 petition for a writ of habeas corpus, asserting that his state-court convictions were obtained in violation of the Fourth Amendment and the Double Jeopardy Clause. We affirm.

I.

The undisputed facts of this case were set forth by the Kentucky Supreme Court as follows:

A. Indictment No. 01-CR-157.

On July 24, 2001, an unidentified caller reported to the Russellville Police Department that two Caucasian males had robbed a boy and fired a weapon at him in the vicinity of Cave Springs Road in Logan County, Kentucky. Law enforcement units from the Kentucky State Police, the Logan County Sheriffs Office, and the Auburn Police Department began searching for the two men. While driving down Gasper River Road, some of the officers passed [Fulcherj’s residence and noticed a number of people standing in the yard, all of whom, upon observing the marked police vehicles, immediately ran into the woods behind the residence. While giving chase, the officers noticed two marijuana plants growing in [Fulcher’sj’s baek yard and the scent of ammonia emanating from an open window in the residence. Unable to obtain a response to knocks on the door of the residence, the officers sought and obtained a search warrant for the residence and surrounding property.

While the officers were awaiting arrival of the search warrant, [Fulcher] *518 emerged from the residence claiming to have been asleep. The officers ordered him to remain outside until after the warrant was executed. One of the persons who had run into the woods, David Harrison, was apprehended but not charged. Six others, C.J. Anderson, Johnnie Finn, Kandi Finn, Andrea Freeman, Jody Cherry, and Matthew Jones, voluntarily returned to the residence and were subsequently arrested.

The July 24, 2001, search of [Fulcher]’s property was conducted by four Kentucky State Police officers. Outside [Fulcher]’s residence they found (1) the two marijuana plants; (2) two plastic containers containing “pill dough;” a “burn pile” containing (3) several empty punctured Prestone starting fluid cans (the ether is removed by puncturing the bottom of the can), (4) several empty Coleman Fuel cans; (5) two boxes filled with used coffee filters; (6) a glass container containing used coffee filters and three layers of liquid attached by plastic tubing to a sealed ketchup bottle which was “cooking” the liquid in the glass container, i.e., gas was then passing from the ketchup bottle through the plastic tubing into the glass container causing the liquid contents of the container to bubble; and (7) an altered propane tank fitted with a copper valve that had turned a bluish-green color (often caused by a chemical reaction with anhydrous ammonia) and containing a small amount of liquid that field-tested positive for anhydrous ammonia. After field-testing the contents of the propane tank, the officers disabled the tank from future use by puncturing it with bullet holes. The officers concluded that the ketchup bottle attached to the bubbling glass jar was a hydrogen chloride “generator” that was “cooking” the coffee filters in the jar in order to extract the methamphetamine residue remaining from an earlier filtering process. The three layers in the bubbling jar consisted of a powdery substance at the bottom, a salty liquid substance in the middle, and a clear substance at the top. The contents of all three layers subsequently tested positive for methamphetamine.

Inside the residence, the officers found (1) a bottle of denatured alcohol on the bar in the living room and (2) an aluminum foil “boat,” a device commonly used in smoking methamphetamine, in the bedroom. The “boat” contained burn marks (the methamphetamine is placed on the “boat,” which is then heated so that the fumes can be inhaled). In the kitchen, the officers found (3) two funnels and (4) a Mason jar, as well as cans of (5) Liquid Fire and (6) Coleman Fuel, and (7) a glass jar in the refrigerator containing ether. They also found what they believed to be (8) a bowl of liquid anhydrous ammonia in the deep freeze. The odor emanating from this bowl was the odor that had first attracted their attention and prompted them to obtain the search warrant. The officers diluted the substance in the bowl and poured it onto the ground without testing it.

Following the search, [Fulcher] was arrested and charged with manufacturing methamphetamine, possession of anhydrous ammonia in an unapproved container with intent to manufacture methamphetamine, possession of drug paraphernalia, and possession of marijuana. He posted bond and was released.

B. Indictment No. 01-CR-179.

On August 1, 2001, Jody Cherry, one of the persons arrested on [FulcherJ’s property on July 24, 2001, signed a crim *519 inal complaint accusing [Fulcher] of twice threatening to kill him. On August 3, 2001, Captain Wallace Whitaker and Deputy Steve Stratton of the Logan County Sheriffs Office proceeded to [Fulcherjs residence to serve him with arrest warrants for terroristic threatening. Upon their arrival, they saw the same altered propane tank that the state police officers had disabled on July 24, 2001. They also detected a strong odor that Stratton believed was “ammonia or ether.” Based on the presence of this odor and the altered propane tank, the officers obtained a warrant to search [Fulcherjs residence and property.

During the search inside the residence, the officers discovered (1) two plastic containers with powder in the bottom that were still smoking, and two empty plastic liquid dishwasher bottles that had been fitted with tubing and that were still emanating gas. Stratton opined that these items had recently been used as homemade generators to separate methamphetamine from ether during the last stage of the manufacturing process. They also found (2) a rubber hose; (3) salt; and (4) a glass jar containing fluid that later tested positive for the presence of methamphetamine; as well as (5) rolling papers; (6) a piece of burnt aluminum foil; (7) a Berez torch that could be used to heat the foil for smoking methamphetamine or to cook the denatured alcohol off of the powdered ephedrine or pseudoephed-rine; and (8) pipes and syringes with burn residue. In addition, they found (9) a glass jar containing a liquid substance that was emanating an odor that Stratton identified as the odor of anhydrous ammonia, as opposed to, e.g., diluted (aqueous) household ammonia. He also testified that anhydrous ammonia is a hazardous material and that law enforcement procedures in place at that time prohibited its storage or transport to a laboratory. Because the sheriffs office did not possess equipment to field-test the substance, Stratton diluted it •with water and poured it onto the ground.

Outside the residence, the officers located a burn pile containing (1) punctured Prestone starting fluid cans and (2) rubber hose. Under the hood of a junked car, they located (3) a bag full of lithium strips. Based on these findings, they charged [Fulcher] with manufacturing methamphetamine, possession of anhydrous ammonia in an unapproved container with intent to manufacture methamphetamine, and possession of drug paraphernalia.

Fulcher v. Commonwealth, 149 S.W.3d 363, 367-71 (Ky. 2004) (“Fulcher I”).

Following a jury trial, Fulcher was convicted on all the charges levied against him in both indictments: two counts of manufacturing methamphetamine, Ky.Rev.Stat. § 218A.1432(1); two counts of possession of anhydrous ammonia in an unapproved container with intent to manufacture methamphetamine, Ky.Rev.Stat. § 250.489; two counts of possession of drug paraphernalia, Ky.Rev.Stat. § 218A.500(2); and one count of possession of marijuana, Ky.Rev.Stat. § 218A.1422. Fulcher I, 149 S.W.3d at 366. Fulcher was thereafter sentenced to 30 years’ imprisonment. Id. at 367.

Following sentencing, Fulcher presented several claims of error before the Kentucky Supreme Court, including violation of the Double Jeopardy Clause. Specifically, Fulcher asserted that “the convictions of separate offenses occurring on July 24, 2001, and August 3, 2001, were premised upon the same evidence[.]” Id. In addition, Fulcher challenged the sufficiency of the evidence, the jury instruc *520 tions, an evidentiary ruling, and a sentencing enhancement. Id.

Upon review, the Kentucky Supreme Court reversed both of Fulcher’s manufacturing convictions, holding that Fulcher did not possess the necessary chemicals and equipment to be convicted under a “possession” theory, requiring retrial on an “actual manufacture” theory. Id. at 370-74. The court also reversed Fulcher’s conviction for possession of anhydrous ammonia in an unapproved container on August 8, holding that the jury instructions improperly allowed the jury to consider the disabled propane tank 'left after the July 24 search. Id. at 375. This charge was also remanded for retrial. The court affirmed Fulcher’s convictions for possession of drug paraphernalia on both July 24 and August 3. Id. at 381. Finally, the court affirmed Fulcher’s convictions for possession of marijuana and possession of anhydrous ammonia in an unapproved container on July 24. Id.

Upon remand, Fulcher moved to suppress evidence stemming from both the July 24 and August 3 searches. This motion was denied, and the case proceeded to retrial. Fulcher was reconvicted of possession of anhydrous ammonia in an unapproved container and manufacturing methamphetamine on August 3. In addition, Fulcher was convicted of complicity to manufacture methamphetamine on July 24. Fulcher v. Commonwealth, Nos.2005-SC-000883-MR, 2005-SC-000952-TG, 2007 WL 1536854, at *1 (Ky. May 24, 2007) (“Fulcher II”). Upon resentencing, Ful-cher received a total sentence of 49 years’ imprisonment, 19 years longer than his initial sentence. Id. at *1.

Following sentencing, Fulcher once again pursued a direct appeal, challenging the denial of his motion to suppress, the sufficiency of the evidence supporting his convictions, the trial court’s refusal to instruct the jury on facilitation, and an evi-dentiary ruling. Id. at *3-*7. The Kentucky Supreme Court found no merit in these claims and affirmed Fulcher’s convictions and sentence. Id. at *8.

On April 14, 2008, Fulcher filed the present petition for a writ of habeas corpus. This petition presents four grounds for relief: (1) “conviction obtained by use of evidence gained pursuant to an unconstitutional search and seizure”; (2) use of “evidence obtained pursuant to an unlawful arrest”; (3) “conviction obtained by the unconstitutional failure of the prosecution to disclose to the defendant [evidence] favorable to [the] defense”; and (4) “conviction obtained by violation of the protection against Double Jeopardy.” Upon respondents’ motion for summary judgment, a magistrate judge recommended that the motion be granted and the petition be denied. Specifically, the magistrate found that Fulcher’s Fourth Amendment claims were not cognizable on habeas review and that the remaining claims were procedurally defaulted. After consideration of Ful-cher’s objections, the district court adopted the magistrate’s report and recommendation. This timely appeal followed. 1

II.

We review the district court’s habeas decision de novo. Souter v. Jones, 395 F.3d 577, 584 (6th Cir. 2005). The Antiter-rorism and Effective Death Penalty Act of 1996 (“AEDPA”) supplies the limitations of federal habeas review of state court proceedings. Under AEDPA, an application *521 for a writ of habeas corpus shall not be granted with respect to any claim that was adjudicated on the merits in state court proceedings unless adjudication of the claim:

(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or

(2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.

28 U.S.C. § 2254(d); Harris v. Haeberlin, 526 F.3d 903, 909 (6th Cir. 2008).

III.

Fulcher asserts that the Kentucky courts erred in rejecting his Fourth Amendment claims. Such claims, however, are not generally cognizable on habeas review. Indeed, “where the State has provided an opportunity for full and fair litigation of a Fourth Amendment claim, the Constitution does not require that a state prisoner be granted federal habeas corpus relief on the ground that evidence obtained in an unconstitutional search or seizure was introduced at his trial.” Stone v. Powell, 428 U.S. 465, 482, 96 S.Ct. 3037, 49 L.Ed.2d 1067 (1976).

In order to determine whether a petitioner received a “full and fair” opportunity to litigate a Fourth Amendment claim, we apply a two-part test. First, we “must determine whether the state procedural mechanism, in the abstract, presents the opportunity to raise a fourth amendment claim[,]” and second, we “must determine whether presentation of the claim was in fact frustrated because of a failure of that mechanism.” Riley v. Gray, 674 F.2d 522, 526 (6th Cir. 1982). In performing this analysis, we do not review the “correctness” of the state court decision. Id.

Upon review, we hold that Fulcher had a full and fair opportunity to litigate his Fourth Amendment claims in state court. As his primary argument, Fulcher asserts that the Kentucky State Police acted in bad faith in obtaining the August 3 search warrant, which he contends was not supported by probable cause. This precise issue, however, was addressed at trial and reviewed by the Kentucky Supreme Court. Fulcher II, 2007 WL 1536854, at *3-*4. Moreover, there is no evidence indicating that Fulcher’s presentation of his claim was somehow frustrated. Accordingly, Fulcher’s arguments before this court, which go to the “correctness” of the Kentucky Supreme Court’s analysis, will not be considered. Riley, 674 F.2d at 526.

With regard to the July 24 search, Ful-cher again asserts that the warrant was not supported by probable cause. This claim, like the first, is not cognizable on habeas review as Fulcher had a “full and fair” opportunity to litigate this claim in state court. Id. What’s more, this claim is procedurally defaulted, as Fulcher failed to challenge the July 24 search on direct appeal and he may no longer assert the claim in state-court proceedings. Fulcher II, 2007 WL 1536854, at *3 n. 1. Accordingly, the claim is barred.

IV.

In his next claim of error, Fulcher asserts that the jury’s consideration of the same evidence to support multiple convictions violated the Double Jeopardy Clause. Specifically, he asserts that evidence left behind by officers after the July 24 search formed the basis for his convictions based on the August 3 search. This claim is •without merit for several reasons.

First, Fulcher forfeited this claim. In his habeas petition, with regard to double jeopardy, Fulcher stated: “The prose *522 cution used the same evidence in both charges to obtain the conviction of 19 more years in the second trial than in the first trial of 30 years, for a total of 49 years.” This statement demonstrates that Fulcher took issue with his longer sentence upon retrial, not the use of the same evidence to obtain multiple convictions.

In addressing Fulcher’s double jeopardy claim, the magistrate framed the issue as follows: “[cjonviction obtained by a violation of the protection against double jeopardy inasmuch as he received more years on retrial.” The magistrate did not address the duplicative consideration of evidence, and Fulcher did not object to this omission. Accordingly, Fulcher has forfeited this issue on appeal. See United States v. Walters, 638 F.2d 947, 949-50 (6th Cir. 1981).

Moreover, even apart from the forfeiture, Fulcher has procedurally defaulted his double jeopardy claim with regard to two out of his three convictions stemming from the August 3 search. These convictions were one count of manufacturing methamphetamine, one count of possession of anhydrous ammonia in an unapproved container, and one count of possession of drug paraphernalia. As Fulcher points out, he directly appealed his first set of convictions to the Kentucky Supreme Court and presented a double jeopardy claim based upon the duplicative consideration of evidence. Fulcher I, 149 S.W.3d at 374. That court held that the use of duplicative evidence was not a violation of double jeopardy with regard to his possession of drug paraphernalia and affirmed the August 3 conviction. Fulcher’s convictions for manufacturing methamphetamine and possession of anhydrous ammonia in an unapproved container on August 3 were both reversed and remanded. Id. at 375. Following retrial, Fulcher was again convicted of these crimes. However, upon direct review of these convictions, Fulcher did not present a double jeopardy claim, resulting in procedural default. Coleman, 501 U.S. at 731, 111 S.Ct. 2546; Hartman, 492 F.3d at 358.

We disagree with Fulcher’s assertion that it was unnecessary to reassert the double jeopardy claim in his second direct appeal. This court lacks jurisdiction over claims “not fairly presented to the state courts.” Blackmon v. Booker, 394 F.3d 399, 400 (6th Cir. 2004). The very purpose of the exhaustion requirement is to “give the state courts an opportunity to act on [a petitioner’s] claims before he presents those claims to a federal court in a habeas petition.” O’Sullivan v. Boerckel, 526 U.S. 838, 842, 119 S.Ct. 1728, 144 L.Ed.2d 1 (1999). Here, Fulcher did not assert before any Kentucky court that his convictions upon retrial were procured in violation of the Double Jeopardy Clause. Accordingly, the claim was left unexhausted and is now procedurally defaulted. See King v. Reynolds, 77 F.3d 492, 1996 WL 77034, at *2 (10th Cir. 1996) (Table).

This leaves Fulcher’s conviction for possession of drug paraphernalia on August 3. Before the Kentucky Supreme Court, Fulcher asserted that this conviction was improperly obtained through the jury’s consideration of the same evidence used to obtain his July 24 conviction. The court rejected this argument, holding that the continuous possession of drug paraphernalia allows for more than one conviction when the possession is “interrupted” by legal process. Fulcher I, 149 S.W.3d at 376-78. Fulcher does not argue that this holding constitutes an unreasonable application of clearly established federal law or involves an unreasonable determination of fact. 28 U.S.C. § 2254(d). Rather, he merely asserts, without developed argumentation, that the jury’s consideration of the same evidence to convict him of two *523 separate crimes constitutes double jeopardy. Accordingly, this argument is forfeited. See Taylor v. McKee, 649 F.3d 446, 452 (6th Cir. 2011) (“[Ijssues adverted to in a perfunctory manner, unaccompanied by some effort at developed argumentation, are deemed waived.”) (internal quotation marks and citation omitted).

Moreover, even if Fulcher had not forfeited his challenge of the Kentucky Supreme Court’s analysis, any such challenge would fail. We may grant habeas relief only if the state-court decision “was contrary to, or involved an unreasonable application of, clearly established Federal law,” or “resulted in a decision that was based on an unreasonable determination of the facts.” 28 U.S.C. § 2254(d). There is nothing in the record to indicate that the Kentucky Supreme Court made an unreasonable determination of fact, and its application of federal law was not unreasonable.

The Double Jeopardy Clause provides that no person shall “be subject for the same offence to be twice put in jeopardy of life or limb.” U.S. Const., amend. V. 2 Generally, “continuous and uninterrupted possession” of contraband may be the subject of only one criminal prosecution. United States v. Jones, 533 F.2d 1387, 1390 (6th Cir. 1976) (citing Ex parte Snow, 120 U.S. 274, 281-86, 7 S.Ct. 556, 30 L.Ed. 658 (1887)). The Kentucky Supreme Court held that Fulcher’s possession of drug paraphernalia, first discovered on July 24, was interrupted by legal process, allowing for an additional prosecution. Although the Supreme Court has not directly addressed this issue, the federal circuit courts have consistently held that a continuous course of conduct, such as possession of an illegal item, may be interrupted so as to allow for multiple convictions. See, e.g., United States v. Conley, 291 F.3d 464, 470 (7th Cir. 2002); United States v. Rivera, 77 F.3d 1348, 1351-52 (11th Cir. 1996). Indeed, we have previously held that:

The return of an indictment charging a course of conduct prevents the relitigation of any course of conduct charged in the indictment which is tried or dismissed with prejudice and which occurred prior to the return of the indictment. However, it does not cut off the ability of the Government to charge a course of conduct subsequent to the indictment which also establishes possession of the same contraband.

Jones, 533 F.2d at 1391. In this case, it is unclear whether Fulcher was actually indicted for his July 24 conduct prior to the August 3 search. Nevertheless, the Kentucky Supreme Court held that Fulcher’s arrest was sufficient “legal process” to interrupt his possession. Given that Fulcher has provided no contrary authority, we hold that this finding is not an unreasonable application of clearly established federal law.

V.

In his final claim, Fulcher asserts that the Kentucky courts violated double jeopardy when he received a substantially higher sentence upon retrial. This claim, however, was not raised on direct appeal. Accordingly, it is procedurally defaulted. Coleman, 501 U.S. at 731, 111 S.Ct. 2546; Hartman, 492 F.3d at 358. Moreover, even if we were to address this claim, it is clearly without merit. Upon retrial, a jury is not precluded from imposing a higher sentence than that initially imposed. Chaffin v. Stynchcombe, 412 *524 U.S. 17, 18, 93 S.Ct. 1977, 36 L.Ed.2d 714 (1973). Thus, Fulcher is not entitled to habeas relief on this claim.

VI.

For the foregoing reasons, we affirm the district court’s denial of Fulcher’s habeas corpus petition.