# nt.number theory – Counting squares modulo \$p\$ that are also prime in an interval

What would be the best lower bound for the number of squares modulo $$p$$ in an interval $$[1,N]$$ with $$N that are prime?
Via the Burgess bound, I can find a lower bound for the number of squares modulo $$p$$ in $$[1,N]$$, but I would need a bound for the number of squares that are also prime. Since the size of $$N$$ matters, in my particular case I have
$$N=frac{sqrt{p}}{2}.$$
Thank you very much!