I think others misunderstand your question, and while I do not have time ot answer completely, I think I can clarify.
I think you are looking for a listing of all aircraft that have been given a fighter (F) designation, including prototypes, like this:
F-4 Phantom II
F-5 Freedom Fighter / F-5E and F-5F Tiger II
and so on, including prototypes
F-16 Fighting Falcon
F-17 Cobra (actually the YF-17)
F/A-18 Hornet
There are some complications: the designation series was restarted in 1962 to include Naval aircraft, so prior to that the Air Force fighters were all the way up to the 110's, and the Navy fighters used a different system that included the manufacturer. An F4F was a WWII Wildcat, while the F4H was the Phantom II. In addition, "F"'s used to be "P" (Pursuit), so many of the planes that were active at and immediately after the end of WWII were re-designated. For Example the P-80 became the F-80.
If you are looking for every fighter design including the "P"'s, the Pre 1962 Navy "F"s, it''s hundreds of aircraft models. Feel free to Google and build your list.