Proof of a conjectural supercongruence

Let $m>2$ and $q>0$ be integers with $m$ even or $q$ odd. We show the supercongruence $$\sum _{k=0}^{p-1}(-1{)}^{km}{\left(\genfrac{}{}{0px}{}{p\mathrm{/}m-q}{k}\right)}^m\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}{p}^3)\mathrm{.}$$ for any prime $p>mq$. This confirms a conjecture of Sun.