  In this paper we introduce a variant of weight modules for certain conformal
vertex superalgebras as an appropriate framework of the $\mathcal{N}=2$
supersymmetric coset construction. We call them weight-wise admissible modules.
Motivated by the work of Feigin-Semikhatov-Tipunin, we give (block-wise)
categorical equivalences between the categories of weight-wise admissible
modules over $\widehat{\mathfrak{sl}}_{2}$ and the $\mathcal{N}=2$
superconformal algebra, induced by the coset construction. As an application,
we obtain some character formulae of modules over the $\mathcal{N}=2$
superconformal algebra.
