In this article, we explore the problem of determining isomorphisms between the twisted complex group algebras of finite p-groups. This problem bears similarity to the classical group algebra isomorphism problem and has been recently examined by Margolis-Schnabel. Our focus lies on a specific invariant, referred to as the generalized corank, which relates to the twisted complex group algebra isomorphism problem. We provide a solution for non-abelian p-groups with generalized corank at most three.