Vehicular　fog　computing　(VFC)　is　a　powerful　technology　that　extends　fog　computing　to　regular　vehicular　networks,　providing　end-users　and　vehicles　with　ultra-low-latency　services.　It　enables　connected　Vehicular　Fog　Nodes　(VFNs)　to　process　real-time　data　and　promptly　respond　to　user　queries.　However,　touching　unencrypted　data　by　VFNs　raises　security　challenges　definitely,　the　top　of　which　is　confidentiality,　and　giving　encrypted　data　to　VFNs　causes　other　problems　such　as　encrypted　data　processing.　Apart　from　these,　how　to　inspect　and　encourage　VFNs　to　provide　a　secure,　honest,　and　user-satisfactory　network　is　of　vital　importance　to　this　area.　To　address　these　challenges,　we　design　a　novel　fine-grained　data　management　(FGDM)　approach　for　VFC-assisted　systems.　Our　FGDM　provides　control　over　both　retrieval　and　access　to　outsourced　data　in　fine-grained　ways.　Also,　it　offers　highly　efficient　approaches　for　the　accuracy　verification　of　operations　performed　by　VFNs.　In　designing　the　system,　we　consider　a　three-player　game　among　system　entities　to　capture　their　interactions.　We　formulate　the　management　problems　as　a　Nash　Equilibrium　(NE)　problem　and　show　the　existence　of　an　equilibrium.　Our　security　analysis　and　empirical　results　demonstrate　that　the　FGDM　is　secure　in　the　standard　model　and　acceptably　efficient.　Our　scheme’s　performance　is　rigorously　assessed,　offers　improved　speed,　and　is　cost-effective　compared　to　existing　methods.　It　reduces　computational　and　communication　costs,　achieving　a　reduction　of　nearly　25%　compared　to　comparable　designs.　©　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature　2023.