  In this work, we analyze an extended $\mathcal{N}=2$ supersymmetry with
central charge and develop its superspace formulation under two distinct
viewpoints. Initially, in the context of classical mechanics, we discuss the
introduction of deformed supersymmetric derivatives and their consequence on
the deformation of one-dimensional non-linear sigma model. After that,
considering a field-theoretical framework, we present an implementation of this
superalgebra in two dimensions, such that one of the coordinates is related to
the central charge. As an application, in this two-dimensional scenario, we
consider topological (bosonic) configurations of a special self-coupled matter
model and present a non-trivial fermionic solution.
