Fixed-time synchronization of Markovian switching stochastic complex networks via quantized aperiodically intermittent control is studied by this article. To achieve synchronization, a new control law is proposed. This control law greatly decreases the control expenses by saving communicating access and communicating bandwidth. By structuring Lyapunov functionals, and applying a designed comparison system, some simultaneity results are presented in terms of using the characteristics of Wiener processes. Comparatively speaking, there are two main features of this article. 1) Markov processes are applied to switching stochastic topological systems. 2) Fixed-time synchronization is achieved by a quantized intermittent controller to save resources. Finally, the result of the numerical simulation verifies the validity of the theoretical analysis.