  This work provides the first step toward the classification of irreducible
finite weight modules over twisted affine Lie superalgebras. We study all such
modules whether the canonical central element acts as a nonzero multiple of the
identity map or not. Moreover, we reduce the classification of some subclasses
of irreducible finite weight modules to the classification of cuspidal modules
of finite dimensional cuspidal superalgebras which is known by a work of
Dimitrov, Mathieu and Penkov.
