The latest wireless gaming controller for you iOS and Apple TV is the Horipad Ultimate. This is the second MFi controller by Hori USA, currently retailing at $49.95 which seems reasonable relative to the earlier price points nearing $100.
The Horipad Ultimate includes dual analog sticks, shoulder buttons, four face buttons, and a D-Pad. Although it is compatible for iOS devices, it doesn’t include a clamp to hold your mobile device. Thus, you will require a stand or case in order to game with the Horipad Ultimate.
It is a wireless controller with a rechargeable lightning port. A full battery will last upwards to 80 hours.
There are hundreds of compatible games for MFi-controllers, many listed over at AfterPad. Dig through the catalog and try gaming with a controller.
See it in the Apple Store here. Online orders take 1-2 business days.