The cooperative output regulation problem for heterogeneous multi-agent systems under sensor and actuator attacks with an adaptive self-triggering strategy is considered in this article. The attack considered is the false data injection attack. To resolve the system, a dynamic internal model is introduced for each agent, and a distributed adaptive self-triggering control scheme is proposed. The results show that intermittent communication is possible for all agents using the proposed control mechanism and no agent shows Zeno behavior. The adaptive controller is used to guarantee that the regulated output for the heterogeneous multi-agent systemss is achieved with cooperative uniform ultimate boundedness under both actuator and sensor attacks. Given the whole state of information is unavailable, the adaptive dynamic system is designed based on receivable compromised or uncompromised output information. The effectiveness of the given control scheme is illustrated by two examples.