A C172 Flight Instructor reported a NMAC with a military fighter jet on short final.

Narrative

It was my first flight of the morning at ZZZ; where I have flown many hours. They randomly have military fighter flights there and try to either ground GA; or move us to opposite side of the air field. On our downwind for runway XX I was cleared to land; and then shortly after to make right traffic. Which I repeated. Once I turned onto the base they gave me additional instructions when I got to the right crosswind leg. From what I remember it was on the crosswind continue on downwind and they were going to give me further instructions for spacing in order to get Aircraft Y into land. So I continued to final with no word from tower; and about 300AGL Aircraft Y passed about 200Ft over top of me. Later I found out that what tower gave me and what was meant was very confusing to both me and the Aircraft Y pilot; and should have been something different. I have been there many times when military fighters where in the area; and normally if they are trying to provide separation it's sounds something like this. Aircraft X I have Aircraft Y inbound to land; cancel clearance to land; and I want you to continue through final; and join the opposite down wind and expect further instructions for spacing. Definitely always try to stay clear of the military fighter pilots; and try to avoid them at all cost.