World invasion fic/beast invasion fic. Except its a version of our world where instead of the games being released in 1996 portals opened around the world and pokemon came through.
So there's the whole genre of fics where portals (or dungeons/towers, for a more contained invasion) suddenly appeared around the world one day and soon humanity was overwhelmed with beast tides and monsters, etc.
Humanity falls back to walled/fortress cities and things look grim, but then humanity gains powers and/or learns to tame the beasts and they begin to fight back and adapt to the new state of the world.
So take all of that, but give it the pokemon spin.
The "powers" people gain could be aura users/psychics/hex maniacs, as well as humanity just in general becoming stronger/sturdier as time/generations go by (as per the ridiculous fears ash and others do in the anime/comics when paired with the lore for Pokémon weights/etc, and surviving).
The "monsters" are Pokémon, so of course there will be those that will form bonds with humanity/help them fight back against others.
There are Swarms/migrations/etc in the games, so those (combined with them still adapting to/moving into Earth) could be beast tides.
Various final evolutions and/or psuedo legendary species' territories become "Forbidden zones". Not to mention actual Legendaries and how humanity would react to them/how the Legendaries would react to (Earth) Humans/modern weapons. (Only take the first nuke before one of them would remove them from the world or something)
(Also, whether or not the world the Pokémon are coming from has its own humans or if these ones have never before met humanity, both could be interesting)