Classification of simple quasifinite modules for contact superconformal algebras with $N\mathrm{\ne }4$

In this paper, we classify all simple jet modules for contact superconformal algebras $\mathcal{K}(N;\epsilon )$ with $N\mathrm{\ne }4$. Then all simple quasifinite modules for $\widehat{\mathcal{K}}(N;\epsilon )$ ($N\mathrm{\ne }4$), the universal central extension of $\mathcal{K}(N;\epsilon )$, are classified. Our results show that Matínez-Zelmanov’s conjecture in \cite{MZe1} holds for $\mathcal{K}(N;\epsilon )$ ($N\mathrm{\ne }4$).