Careful　consideration　of　grid　developments　illustrates　the　fundamental　changes　in　its　structure　which　its　developments　have　taken　place　gradually　for　a　long　time.　One　of　the　most　important　developments　is　the　expansion　of　the　communication　infrastructure　that　brings　many　advantages　in　the　cyber　layer　of　the　system.　The　actual　execution　of　the　peer-to-peer　(P2P)　energy　trading　is　one　core　advantage　which　also　may　lead　to　the　systematic　risks　such　as　cyber-attacks.　Consequently,　it　is　necessary　to　form　a　useful　way　to　cover　such　challenges.　This　paper　focuses　on　the　online　detection　of　false　data　injection　attack　(FDIA),　which　tries　to　disrupt　the　trend　of　optimal　peer-to-peer　energy　trading　in　the　stochastic　condition.　Moreover,　this　article　proposes　an　effective　modified　Intelligent　Priority　Selection　based　Reinforcement　Learning　(IPS-RL)　method　to　detect　and　stop　the　malicious　attacks　in　the　shortest　time　for　effective　energy　trading　based　on　the　peer　to　peer　structure.　The　presented　method　is　compared　with　other　methods　such　as　support　vector　machine　(SVM),　reinforcement　learning　(RL),　particle　swarm　optimization　(PSO)-RL,　and　genetic　algorithm　(GA)-RL　to　validate　the　functionality　of　the　method.　The　proposed　method　is　implemented　and　examined　on　three　interconnected　microgrids　in　the　form　of　peer-to-peer　structure　wherein　each　microgrid　has　various　agents　such　as　photovoltaic　(PV),　wind　turbine,　fuel　cell,　tidal　system,　storage　unit,　etc.　Eventually,　the　unscented　transformation　(UT)　is　applied　for　uncertainty　analysis　and　making　the　near-reality　simulations.