Does PUBG need an introduction?
PlayerUnknown's Battleground took the world by storm and the only thing more popular is probably Fortnite. If you're looking for a great shooter, try PUBG.
And while this game is typically a 3rd person shooter, you can play in FPS mode too. Although personally, I feel like 3rd person gives you an advantage. The idea is simple. They drop 100 players on an island and slowly force everyone to the center. The last player standing wins. It's incredibly fun, addicting, and action-packed.
PUBG is one of the best shooter games for mobile, period.