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 [6]. Then all finite non-trivial irreducible conformal modules over $\mathcal{S}(p)$ for $p\in {\mathbb{C}}^{⁎}$ 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 $n\ge 1$ 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.

在本文中，我们介绍了一类无限李形保角超代数 $\mathcal{小号}（p）$与[6]中定义的扩展Block类型的Lie保形代数密切相关。然后所有有限非平凡不可约保形模块$\mathcal{小号}（p）$ 为了 $p\in {\mathbb{C}}^{⁎}$被完全分类。作为应用，我们还提出了有限商代数上的有限非平不可约保形模块的分类$\mathfrak{s}（ñ）$ 为了 $ñ\ge \mathrm{1个}$ 和 $\mathfrak{SH}$ 与Lie共形代数的子代数同构 $ñ=\mathrm{2个}$超保形代数。而且，作为$\mathcal{小号}（p）$，无限李共形超代数 $\mathcal{GS}（p）$ 构造，其具有与的有限Lie共形代数同构的子代数 $ñ=\mathrm{2个}$ 超保形代数。