C172 instructor pilot reported an NMAC while on a IFR flight plan and approaching the airport using the localizer approach. The instructor stated that the Tower Controller had a Citation jet make a 360 degree turn; 400 feet above their aircraft; to rejoin final. The instructor was ask to call the tower on the ground.

Narrative

On an IFR flight plan into ZZZ with a student under the hood flying the LOC Y Runway XX low approach only. We were on approximately a 2 mile final and at this point a Citation which we had been tracking on our ADS-B was now same altitude off our right wing. They were previously issued an instruction to follow my aircraft and be number two for Runway XX into ZZZ. The Controller in the Tower was asking for multiple position reports from four aircraft inbound to the field. The Controller then issued the Citation a right 360 instruction and rejoin final for Runway XX. This instruction turned the Citation right over the top of my aircraft and the ADS-B in was alerting traffic was 400 ft. directly above us. Following that we were given the instruction to go missed at 800 ft. MSL and 1 mile for the runway. The student executed the missed as instructed by Tower and I informed the Tower of the near midair collision from my perspective and loss of separation. Though I believe the verbiage I used on the radio of the time was 'near miss.' I was then given a phone number to call once on the ground; which I did and spoke with the Controller on duty at the time of the near midair collision. When asked why he turned that aircraft into our flight path; his response was because he didn't want to turn them over the field and they were above us. This entire event could potentially been avoided if the Tower had radar; but they don't and rely on aircraft reporting their positions.