Fix a large positive integer $m$. Let $A$ be small positive number typically $\sim m^{1/3}$. Suppose $S(A, m)$ be set of solutions (normalized by dividing by $m$) to the quadratic congruences $x^2 = a \mod{m}$ such that $0 < x < m$ as $a$ runs from $1$ to $A$. What is known about the distribution of $S(A, m)$ on $[0, 1)$? Does it show any form of equidistribution? If yes then what error terms does it give?