Frank Johnson and Ruth Johnson, a husband and wife proceeding pro se, appeal the district court’s order denying their motion for post-judgment relief, pursuant to Federal Rule of Civil Procedure 60(b), of an order dismissing them 42 U.S.C. §§ 1981 and 1983 civil rights complaint. On appeal, the Johnsons argue that: (1) the district court mistakenly determined that private actors cannot act under color of state law; (2) the defendants committed a fraud on the district court by conspiring with a Florida state court judge; (3) the district court errone *448 ously dismissed their civil rights complaint; and, (4) the district court abused its discretion by denying the Johnsons’ motion for recusal of the district court judge. We find each ax-gument mex-itless. Therefore, we affirm.

We review the distx-iet coux't’s denial of x-elief under Rule 60(b) for an abuse of discx-etion. Big Top Koolers, Inc. v. Circus-Man Snacks, Inc., 528 F.3d 839, 842 (11th Cir. 2008) (citations omitted). However, only the denial of relief as to the motion filed under Rule 60(b) can be eon-sidex’ed, not the undex-lying judgment. Cavaliere v. Allstate Ins. Co., 996 F.2d 1111, 1115 (11th Cir. 1993). Rule 60(b) cannot be used as a substitute for a proper and timely appeal. Id.

Relief is available under Rule 60(b)(1) for mistakes of law or its application. Parks v. U.S. Life & Credit Corp., 677 F.2d 838, 839-40 (11th Cir. 1982) (per cu-i'iam). A party may also file a motion for x’elief from a judgment or order based upon “fraud (whether previously called in-tx-insic or extx-insic), misx-epx-esentation, ox-misconduct by an opposing party....” Fed.R.Civ.P. 60(b)(3). “[Ojnly the most egregious misconduct, such as bribery of a judge or members of a jury, or the fabx-ieation of evidence by a pax-ty in which an attorney is implicated, will constitute a fraud on the court.” Rozier v. Ford Motor Co., 573 F.2d 1332, 1338 (5th Cir. 1978). To prove a fx-aud on the court, the plaintiff must show, by clear and convincing evidence, an unconscionable plan designed to improperly influence the eoux’t in its decision. Id. at 1338-39.

We x-eview a judge’s decision not to re-cuse himself for an abuse of discretion. United States v. Berger, 375 F.3d 1223, 1227 (11th Cir. 2004) (per curiam) (citation omitted). A judge’s x*ulings in the same case generally cannot serve as grounds fox-recusal. See United States v. Meester, 762 F.2d 867, 884 (11th Cir. 1985).

In order to state a claim under 42 U.S.C. § 1983, the defendants must have acted “under color of state law.” This requirement excludes mex-ely private conduct. Focus on the Family v. Pinellas Suncoast Transit Auth., 344 F.3d 1263, 1277 (11th Cir. 2003). We x-ecognize three primary tests to determine whether a px-i-vate pax-ty acted “under color of state law”: “(1) the public function test; (2) the state compulsion test; and (3) the nexus/joint action test.” Id.

The public function test limits state action to instances whex-e px-ivate actox*s are pex-fox-ming functions traditionally the exclusive prerogative of the state. The state compulsion test limits state action to instances where the government has coerced or at least significantly encoux’aged the action alleged to violate the Constitution. The nexus/joint action test applies whex-e the state has so far insinuated itself into a position of interdependence with the [private pax-ty] that it was a joint participant in the entei’px’ise. We must detex-mine on a case-by-case basis whether sufficient state action is px-esent from a non-state actor (defendant) to sustain a section 1983 claim.

Id. (internal quotation marks and citations omitted).

Hex-e, the Johnsons’ conclusory allegations that the defendants conspired with a Flox-ida judge were not enough to transfox’m the defendants into state actors. Thus, the district court did not mistake the law or its application. Furthermore, the Johnsons failed to allege any activities ixx the district court that would constitute fraud or misconduct. Therefore, the district court did not abuse its discx-etion in denying the Johnsons’ motion for post-judgment relief.

The Johnsons’ arguments regarding the dismissal of their civil rights com *449 plaint are not properly before us. Review of a Rule 60(b) motion cannot be used to review the underlying judgment, nor can the Johnsons now use them 60(b) motion as a substitute for a proper appeal.

Lastly, the Johnsons failed to amend their notice of appeal to include the order denying their motion for the district court judge to recuse himself. Accordingly, we lack jurisdiction to consider this order on appeal. Fed. R.App. P. 3; see Green v. Union Foundry Co., 281 F.3d 1229, 1233 (11th Cir. 2002) (declining to hear the appellant’s second post-judgment motion because the appellate “failed to either amend his original notice of appeal or file a separate appeal from the district court’s denial of his second post-judgment motion, and therefore, [appellant had] not properly perfected an appeal from that order”).

Upon consideration of the record and the parties’ briefs, we discern no reversible error. Accordingly, we affirm.

AFFIRMED