Let $P$ denote the set of positive primes and let $p$ be a fixed prime. Then define $q_{p}:=\min{q\in P:p<q,(q/p)=1}$ where $(⋅/p)$ is the Legendre symbol. So for instance $q_{3}=7$, $q_{3}=7$, and $q_{5} = 11$. Is there anything known about $q_{p}$ and specifically are there known bounds on $q_{p}$ as a function of $p$? I am ultimately interested in investigating $\inf\{q_{p}/p:p\in P \}$.

I understand there are some things known about the smallest prime that is a quadratic residue modulo a prime, i.e. least quadratic residue and nonresidue, but this seems to be a different, albeit related, question.