A bit more towards a Pokémon than Tamagotchi since you battle with a party of them, but they're effectively ghosts that inspirit people to do odd things, though you don't "catch" them you "befriend" them.
If you have a spare 20 minutes you can watch the first episode of the show
https://www.youtube.com/watch?v=4lk_rIXlrxg
Might not be one for me…what is a Yo-Kai? Is that some kind of Tamagotchi?