You don't have to do anything special for that. Itch.io doesn't interfere with a game's controller support or lack thereof. Check out each game's setup instructions and/or option menu, as the case may be. For a list of games with controller support, try one of the following:
- https://itch.io/games/input-gamepad
- https://itch.io/games/input-joystick
- https://itch.io/games/input-playstation
- https://itch.io/games/input-x360
- https://itch.io/games/input-wiimote
Hope this helps!