On quadratic residues and nonresidues in difference sets modulo $m$

Let $m > 1$, and consider a set $\mathcal{A} = \{ {a_i}\}$ of residues modulo m such that ${a_i}$ and ${a_i} - {a_j}$ for all i and j with $i \ne j$ are quadratic residues (nonresidues) modulo m. We investigate the estimation of the maximal cardinality of such a set $\mathcal{A}$ for various moduli m.