  Let $R$ be a commutative noetherian ring, $\frak a$ be an ideal of $R$,
$\mathcal{S}$ be an arbitrary Serre subcategory of $R$-modules satisfying the
condition $C_{\frak a}$ and let $\mathcal{N}$ be the subcategory of finitely
generated $R$-modules. In this paper, we define and study $\mathcal{NS}$-$\frak
a$-cofinite modules with respect to the extension subcategory $\mathcal{NS}$ as
an generalization of the classical notion, namely $\frak a$-cofinite modules.
For the lower dimensions, we show that the classical results of $\frak
a$-cofiniteness hold for the new notion.
