With the advent of smart cities, the significance of the Internet of Things (IoT) is gaining greater prominence. At the same time, the safety early warning system in the IoT has a significant impact on real-time monitoring and the response to potential risks. Despite the advancements made in edge-assisted IoT deployments, several challenges and constraints persist. Given the potential threat to life posed by safety-related messages, ensuring the authenticity of messages in the edge-assisted IoT safety warning system is crucial. However, considering the identity privacy of devices participating in the edge-assisted Internet of Things system, directly verifying the identity of the sending device is undesirable. To address this issue, in this work, we design a linkable group signature scheme that allows devices to anonymously send safety-related messages to edge nodes, defending against Sybil attacks while ensuring the traceability of malicious device identities. Then, we present a high-efficiency conditional privacy-preserving authentication (CPPA) scheme based on the designed group signatures for the safety warning system in edge-assisted IoT. This scheme effectively protects device identity privacy while providing a reliable authentication mechanism to ensure the credibility and traceability of alert messages. The proposed scheme contributes to the field of safety warning systems in the context of edge-assisted IoT, providing a robust solution for privacy preservation and authentication.