Ronald Pernell Green, federal prisoner # 09156-035, filed a motion under 28 *347 U.S.C. § 2255 challenging his 1999 drug convictions. On February 21, 2006, the district court denied the motion in part and ordered that a hearing be set on one of Green’s ineffective-assistance-of-counsel claims. On March 3, 2006, Green gave notice of his appeal from the district court’s order and judgment of February 21, 2006. On March 27, 2006, the district court entered its final judgment, granting of the remaining ineffective-assistance claim. Green has applied to this court for a certificate of appealability (COA).

“This Court must consider, sua sponte if necessary, whether appellate jurisdiction exists.” Clark v. Johnson, 278 F.3d 459, 460 (5th Cir. 2002). The partial judgment appealed from was not a final judgment. See 28 U.S.C. § 1291; McLaughlin v. Mississippi Power Co., 376 F.3d 344, 350 (5th Cir. 2004). The appeal does not fit within any of the categories of appealable interlocutory orders listed in 28 U.S.C. § 1292. Nor has the district court certified the judgment for immediate appeal pursuant to Fed.R.Civ.P. 54(b). Although a premature notice of appeal may be deemed timely filed under Fed. R.App. P. 4(a)(2), Green’s appeal does not fit within that rule because the district court had not finally disposed of all of the claims in the partial judgment from which Green appealed. See FirsTier Mortgage Co. v. Investors Mortgage Ins. Co., 498 U.S. 269, 276, 111 S.Ct. 648, 112 L.Ed.2d 743 (1991); United States v. Cooper, 135 F.3d 960, 961-63 (5th Cir. 1998). Nor do we have jurisdiction under the collateral order doctrine because the district court’s judgment did not resolve issues separate from the merits that would unreviewable on appeal from a final judgment. See Cohen v. Beneficial Indus. Loan Corp., 337 U.S. 541, 546, 69 S.Ct. 1221, 93 L.Ed. 1528 (1949). Accordingly, Green’s motion for a COA is denied, and the appeal is dismissed for lack of jurisdiction.

COA DENIED; APPEAL DISMISSED.