Do you mean an actual Pokemon game or a game inspired by Pokemon involving similar mechanics? As long as you're aware of copyrights/trademarks you can do what you want, but I would recommend using existing games as inspiration rather than fully deriving from them or making a fangame. It shows creativity and will be easier for you to expand on later, should you choose to do so.
Pokemon-like games are part of a new-ish genre called Monster Tamers which fit that kinda vibe. Digimon, Coromon, Monster Crown, Monster Sanctuary, Disc Creatures, etc are some good games to check out if you want more ideas!
