A neural network adaptive quantized predefined-time control problem is studied for switching stochastic nonlinear systems with full-state error constraints under arbitrary switching. Unlike previous research on rapid convergence, the predefined-time stability criteria are introduced and established for stochastic nonlinear systems, ensuring the stabilization of the control system within a specified time frame. The chattering issue is avoided and it is split into two limited nonlinear functions using a hysteresis quantizer. To address the full-state error constraint problem, a universal barrier Lyapunov function is presented. The common Lyapunov function approach is used to demonstrate the stability of controlled systems. The results demonstrate that the proposed control method ensures all closed-loop signals are probabilistically practically predefined time-stabilized (PPTS), with the system output closely tracking the specified reference signal. Finally, simulated examples validate the effectiveness of the suggested control technique.