Fundamental Group Schemes of some Quot Schemes on a smooth projective curve

Let $k$ be an algebraically closed field. Let $C$ be an irreducible smooth projective curve over $k$. Let $E$ be a locally free sheaf on $C$ of rank $\geq 2$\mathrm{.}Fixaninteger$d \geq 2$\mathrm{.}Let$$\mathcal{Q}$$ denote the Quot scheme parameterizing torsion quotients of $E$ of degree $d$. In this article we compute the $S$-fundamental group scheme of $\mathcal{Q}$.