The problem of adaptive control for stochastic systems impacted by saturation and dead zone is discussed in this study. Neural networks are incorporated into the design to effectively control the unknown nonlinear functions present in these systems. The non-smooth input saturation and dead-zone nonlinearities are approximated using the non-affine smooth function. Next, the mean-value theorem is applied to derive the affine form. The study develops an adaptive finite-time controller using the backstepping approach, ensuring semi-globally practical finite-time stability for all closed-loop system signals while driving the tracking error to converge within a finite time to a small region around the origin. To illustrate the efficacy of the suggested control strategy, two simulation examples are given.