The McDonnell Douglas F-4 Phantom II is a tandem (two-seat), twin-engined, all-weather, long-range jet interceptor fighter/fighter-bomber originally developed for the United States Navy by McDonnell Aircraft. It first entered service in 1960 with the U.S. Navy. Proving highly adaptable, it was also adopted by the U.S. Marine Corps and the U.S. Air Force, and by the mid-1960s had become a major part of their respective air wings.
The F-4 is only mentioned in Top Gun as the plane used by Maverick's father when he was shot down on the wrong side of enemy lines near Vietnam. However it does appear in the video game Top Gun: Combat Zones as a bonus plane for beating the game & in Top Gun: Hard Lock as a drone during flashback missions.
Yeah, he did it right... Is that why you fly the way you do? Trying to prove something? Yeah, your old man did it right. What I'm about to tell you is classified. It could end my career. We were in the worst dogfight I ever dreamed of. There were bogeys like fireflies all over the sky. His F-4 was hit, and he was wounded, but he could've made it back. He stayed in it, saved three planes before he bought it.
In Top Gun, Viper tells Maverick that he flew with Duke Mitchell while assigned to VF-51 aboard the USS Oriskany, presumably during the Vietnam War. In real life, the F-4 was never assigned to the Oriskany because of the aircraft's size. During the Vietnam War, the Oriskany generally carried, among other aircraft, the F-8 Crusader and the A-4 Skyhawk in its assigned carrier air wing.