  Let $R$ be a commutative noetherian ring, $\frak a$ be an ideal of $R$, $\cS$
be an arbitrary Serre subcategory of $R$-modules and let $\cN$ be the
subcategory of finitely generated $R$-modules. In this paper, we study
$\cN\cS$-$\frak a$-cofinite modules with respect to the extension subcategory
$\cN\cS$ when $\dim R/\frak a\leq 2$. We also study $\frak a$-cofiniteness with
respect to a new dimension.
