In this paper, the local and global existence of mild solutions are studied for impulsive fractional semilinear stochastic differential equation with nonlocal condition in a Hilbert space. The results are obtained by employing fixed-point technique and solution operator. In many existence results for stochastic fractional differential systems, the value of \(\alpha \) is restricted to \(\frac{1}{2} < \alpha \le 1;\) the aim of this manuscript is to extend the results which are valid for all values of \(\alpha \in (0,\,1).\) An example is provided to illustrate the obtained theoretical results.