Finite irreducible conformal modules over the Lie conformal superalgebra $mathcal{S}(p)$

In the present paper, we introduce a class of infinite Lie conformal superalgebras $mathcal{S}(p)$, which are closely related to Lie conformal algebras of extended Block type defined in cite{CHS}. Then all finite non-trivial irreducible conformal modules over $mathcal{S}(p)$ for $pinC^*$ are completely classified. As an application, we also present the classifications of finite non-trivial irreducible conformal modules over finite quotient algebras $mathfrak{s}(n)$ for $ngeq1$ and $mathfrak{sh}$ which is isomorphic to a subalgebra of Lie conformal algebra of $N=2$ superconformal algebra. Moreover, as a generalized version of $mathcal{S}(p)$, the infinite Lie conformal superalgebras $mathcal{GS}(p)$ are constructed, which have a subalgebra isomorphic to the finite Lie conformal algebra of $N=2$ superconformal algebra.