While Naval Aviators– Phantom drivers of VF-21 from the carrier USS Midway— shot down the first MiGs in air-to-air combat over Southeast Asia when they splashed a pair of two North Vietnamese MiG-17s on 17 June 1965, the USAF soon got in the game as well.
Of the 196 MiGs zapped in air-to-air combat over Vietnam, 59 were by a mix of Navy/Marine Corps A1-Hs, F-8C/E/Hs, F-4B/D/Js, and an A-4C (which flamed a MiG-17 with a Zuni rocket!), it was the Air Force that managed the lion’s share, mostly MiG-21s via F-4s.
The below chart via the USAF:
Of course, keep in mind that the USAF’s F-86s shot down an amazing 792 MiG-15s in Korea while the USAAF had over 15,000 aerial victories in WWII– almost exclusively up-close gun actions.