Updating to the latest version of iOS will support all game controllers listed below, the list is in chronological order with the newest supported controllers at the top.
iOS 16.4 > Sony Dualsense Edge™
iOS 16.3 > 8BitDo Controllers
iOS 16.0 > Nintendo Switch
iOS 14.5 > PS5 DualSense & XBX One Series X
iOS 13.0 > PS4 DualShock & XBX One
