Fog-based computation is an interesting computing paradigm developed for giving end users access to real-time services in the Internet of Vehicles (IoV). Achieving safe and effective data sharing is a huge challenge in such a dynamic system architecture. As a promising cryptographic primitive, searchable encryption (SE) aims to maintain data searchability while maintaining data confidentiality. Nonetheless, the majority of current methods are open to attacks by leaking exploitation. So, we develop a fog-based searchable public key encryption scheme (FC-PEMKS) that achieves forward security and multi-keyword search in the IoV network. The security proof shows that our model achieves the indistinguishability of trapdoor and keyword index. The outcomes of the comparative simulations and performance analysis demonstrate the viability and effectiveness of the FC-PEMKS scheme in fog-enabled vehicular networks.