  Let $k$ be an algebraically closed field of characteristic $p > 3$. Let $A$
be an abelian surface over $k$. Fix an integer $n \geq 1$ such that $p \nmid n$
and let $K^{[n]}$ be the $n$-th Generalized Kummer Variety associated to $A$.
In this article we aim to find the $S$-fundamental group scheme and Nori's
fundamental group scheme of $K^{[n]}$.
