What type of claim may not invoke supplemental jurisdiction under § 1367(b)?

The type of claim that may not invoke supplemental jurisdiction under § 1367(b) is one brought by the original plaintiff against a third-party defendant. This section of the U.S. Code specifically restricts the use of supplemental jurisdiction in certain situations, particularly focusing on claims made by plaintiffs against diverse parties that would normally not meet the requirements for federal jurisdiction on their own.

In the context of § 1367(b), the limitation applies to claims that would allow a plaintiff to circumvent the complete diversity requirement by bringing in a party who was not initially part of the case. A third-party defendant is typically introduced to the case by the original defendant, meaning the original plaintiff's claim against this third-party defendant might not qualify for supplemental jurisdiction when it relates to a different jurisdictional basis than that initially invoked by the plaintiff’s original complaint.

Claims made by a defendant against an original plaintiff or counterclaims made by new parties generally do not face the same restrictions under § 1367(b), as they can typically be related to the original jurisdictional issue or can be addressed through different provisions of the law. Additionally, claims related to the original claim but arising from a different jurisdiction may still be viable through supplemental jurisdiction if they are sufficiently related to the original claim