Multi-agent systems (MASs) communicate via networks, which are often subjected to denial-of-service (DoS) attacks. How to enable MASs to resist the effects of DoS attacks has become a critical issue. This paper studies the edge-event-triggered \(H_{\infty }\) consensus control of stochastic nonlinear MASs under DoS attacks. Differentiated asynchronous edge-event-triggered mechanisms (EETMs) for various types of agents are designed under DoS attacks. These mechanisms can effectively reduce unnecessary inter-agent communications, thereby enhancing the efficiency of the system and mitigating the impacts caused by DoS attacks. Furthermore, a consensus control protocol applicable to the aforementioned mechanisms is proposed to tackle the \(H_{\infty }\) mean-square consensus control issue in MASs. Then, it is proven that stochastic nonlinear MASs can achieve \(H_{\infty }\) mean-square consensus under DoS attacks. Moreover, under the EETMs proposed in this paper, Zeno behavior does not occur in the system. Finally, through the simulation example, the validity of the theory proposed in this paper is corroborated.