iff condition for quadratic residue modulo p when $p\equiv3\mod 4$

Question

Let $p$ be an odd prime, then we either have $p\equiv 1\mod 4$ or $p\equiv 3\mod 4$. And we have an iff condition for quadratic residue modulo p when $p\equiv 1\mod 4$, which is "$x^2\equiv-1\mod p$ iff $p\equiv 1\mod 4$". I wonder if there is any similar result for $p\equiv 3\mod 4$