OpenID Connect has revolutionized online authentication based on single sign-on (SSO) by providing a secure and convenient method for accessing multiple services with a single set of credentials. Despite its widespread adoption, critical security bugs in OpenID Connect have resulted in significant financial losses and security breaches, highlighting the need for robust mitigation strategies. Automated program repair presents a promising solution for generating candidate patches for OpenID implementations. However, challenges such as domain-specific complexities and the necessity for precise fault localization and patch verification must be addressed. We propose AuthFix, a counterexample-guided repair engine leveraging LLMs for automated OpenID bug fixing. AuthFix integrates three key components: fault localization, patch synthesis, and patch verification. By employing a novel Petri-net-based model checker, AuthFix ensures the correctness of patches by effectively modeling interactions. Our evaluation on a dataset of OpenID bugs demonstrates that AuthFix successfully generated correct patches for 17 out of 23 bugs (74%), with a high proportion of patches semantically equivalent to developer-written fixes.