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In this paper, we introduce some concepts of square-mean S-asymptotically$\omega$-periodic stochastic processes. Using the stochastic analysis methodand the Banach contraction mapping principle, we establish the existence anduniqueness results of the mild solution and the square-mean S-asymptotically$\omega$-periodic solution for a semilinear nonautonomous stochastic fractionalevolution equation driven by L\'{e}vy noise.

Square-mean S-asymptotically $\omega$-periodic solution for a stochastic  fractional evolution equation driven by L\'{e}vy noise with piecewise  constant argument