The current study investigates the exponential synchronization (ES) problem for a class of Markovian jump neural networks (MJNNs), which are susceptible to distributive and additive time-varying delays and are managed by a memory-sampled data controller (MSDC). The transition probabilities in question are thought to be partially unknown. The information of time delay and sampling instants is captured by enhanced Lyapunov-Krasovskii functionals (LKFs). A novel modified integral inequality is utilized, which provides a potent framework for studying dynamical systems, and also made a foundation of this study. Adequate requirements for the ES of proposed system are obtained in the form of linear matrix inequalities (LMIs) by incorporating these integral inequalities. Under these circumstances, the hybrid closed-loop system's mean square input-to-state stability (ISS) is ensured. Lastly, the accuracy of the proposed ISS synchronization mechanism is verified and illustrated with numerical examples.