This hardware item is an unlicensed variation or imitation of the PlayStation Controller.
The Jogcon is a controller developed and produced by Namco for the Sony PlayStation videogame console.
Originally released in 1998 as part of a special edition package with Namco's R4: Ridge Racer Type 4 videogame, it was designed to combine the function of a steering wheel controller, while maintaining the size of a standard PlayStation controller. This is accomplished by a dial approximately 3 inches in diameter in the center of the controller (almost in the same location as the DualShock analog sticks).
The Jogcon would later be sold separately from the Ridge Racer R4 game.
Source: Wikipedia, "Jogcon", available under the CC-BY-SA License.