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In this paper we introduce a variant of weight modules for certain conformalvertex 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 admissiblemodules 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.

Equivalences between weight modules via $\mathcal{N}=2$ coset constructions