Northrop originally built the F-5 "Freedom Fighter" (and T-38 "Talon") with two engines. Later it was re-fitted with a single F404 engine from the F/A-18, re-designating it the F-20 "Tigershark" to avoid confusion. The first F-5A and T-38 flights took place in 1959.
[Addendum: There is no real contradiction, the T-38 "Talon" was a two place trainer version of the F-5 "Freedom Fighter". Most aircraft don't re-designate between one and two seat versions, but Northrop or the military did in this case.] See the history of the F-5 YouTube Video
"Though the USAF had no acknowledged need for a light fighter, it did procure roughly 1,200 Northrop T-38 Talon trainer aircraft, which were directly based on the F-5A." https://en.wikipedia.org/wiki/Northrop_F-5
"The F-5G was an advanced single-engined variant later renamed the F-20 Tigershark." https://en.wikipedia.org/wiki/Northrop_T-38_Talon
Have any other fighters (world wide) offered a fighter with one and two engine models?
Twin engine F-5 "Freedom Fighter".
Single engine F-20 (F-5G) "Tigershark". Wikipedia