<p>This paper focuses on the observer-based adaptive event-triggered quasi-synchronization issue of Markov jump neural networks with energy-limited mixed-type attacks. First, a hidden Markov model is employed to establish the connection between the asynchronous modes of the heterogeneous system. Second, a novel attack-resistant adaptive event-triggered scheme is improved to deal with denial of service attacks by recording the successful release instant, which not only conserves communication resources but also enhances communication security. Next, sufficient conditions for adaptive event-triggered quasi-synchronization of the Markov jump neural networks are established by appealing to Lyapunov techniques. Furthermore, an iterative algorithm with variable step sizes is introduced to optimize the error bound and reduce computational costs. Finally, a numerical example is presented to validate the effectiveness of the proposed iterative algorithm and observer-based control scheme.</p>