There were a total a 269 American and enemy aircraft shot down in air-to-air combat over Vietnam during the entire war—201 in fights between the U.S. Air Force and North Vietnamese air force and just 68 in the U.S. Navy’s air battles with the North Vietnamese.

Democratic Republic of Vietnam Aircraft Russian source: 65 MiG-21s, 5 MiG-19s, 75 MiG-17s lost through all causes.

85 MiGs

Helicopter Losses During the Vietnam War 1,925 Hueys were lost in combat, while 1,380 were lost in operational accidents.

Vietnam’s deadliest job “I can tell you that the engineer corp lost more people, killed and wounded, than any other corp in Vietnam — proportionate to the number of people who were over there,” he said. Mr McGregor said the engineers were highly regarded during the war but were ignored when they returned home.

So Yes. A Soviet Helicopter has shot down American jet fighter in Afghan airspace in the 1980s. Given that Helicopters are harder to spot for jet fighters than vice versa and can carry similar Air to Air missiles I would say it is more than likely that a Helicopter can shoot down a jet fighter.

Iran–Iraq War and helicopter dogfight The Iran–Iraq War also saw the worlds only confirmed helicopter dogfights, with Iranian Army Aviation’s AH-1J Internationals (usually the TOW-capable ones) entering combat mostly against Iraqi Army Air Corps’ Mil Mi-24 Hind gunships and HOT-armed Aérospatiale Gazelles.

AMRAAM missiles can only be fired by F-16s in the PAF inventory. Both the IACCS (Integrated Air Command & Control System) and the Phalcon AWACS registered the radar signature of one MiG-21, piloted by Wing Commander Abhinandan Varthaman, cross the Line of Control and engage an F-16 with a R-73 missile.

Both Syrian and Turkish forces confirmed the downing. On 3 March 2020, a Syrian Arab Army Air Force L-39 combat trainer was shot down by a Turkish Air Force F-16 over Syrian Idlib province. Both Syrian and Turkish forces confirmed the downing. The pilot died.

F6F Hellcat. The F6F was designed to improve on the Wildcat’s ability to counter the Mitsubishi A6M Zero and help secure air superiority over the Pacific Theater. Hellcats were credited with 5,223 kills, more than any other Allied naval aircraft.