I read about quite decent results about distributions of quadratic residues and nonresidues for primes of form $4k+1$ and $4k+3$. For example Dirichlet in 1830's proved that:
Are there analog results when we divide primes not into $4k+1$ and $4k+3$ but for example $6k+1$ and $6k+5$ et cetera? Of course each prime > 2 is of form $4k+1$ or $4k+3$ but maybe there are stronger results for intervals when we know reminder of our prime modulo a lot of natural numbers?