New Controller feature

Just google "apple ios13 controller support games" and you will see a full list, it does include free games.

For example: Dead Trigger 2, Cod Mobile was supported (it was removed today, but might be added back later).

Many popular games will adapt controller support in the future I believe :)

There is not a published list of games that support a controller. You will just have to keep searching for games.

Well when you sign up for the free trial of Apple Arcade ALL the games are free to download and try - at least during the 30 day trial period. And each game lists the number of players and if it supports game controllers in the description in the Apple Arcade app.