C152 flight Instructor reported a NMAC in the traffic pattern occurred when another aircraft flew directly over them in the downwind leg. The flight Instructor took evasive action and then exited the traffic pattern.

Narrative

I was conducting a training flight with a student at ZZZ when this occurred. We were conducting touch and go's on Runway XX. After a few laps in the pattern we were on the departure leg when I heard a radio call that a Yak aircraft was 3 NM southwest of the airport and that they were inbound to enter left traffic Runway XX at 2;000 ft. Very shortly after we made a radio call that we were turning left crosswind for Runway XX and began making the cross wind turn. We did not have visual contact with the Yak. Yak made a call that they had the 'departing traffic in sight'. We proceeded to make the downwind turn and radio call for Runway XX.Shortly after we turned downwind the Yak announced they were also turning downwind. At that point an ADS-B traffic advisory popped up our GPS. The ADS-B traffic showed the Yak at our 6 O'clock position at the same altitude and closing. Another pilot in the traffic pattern announced on CTAF that the Yak was right on top of us and use caution. At that point I announced on CTAF that I would be making a right 360 turn for spacing and that we would follow in behind the Yak.The Yak announced that they couldn't see us and thanked us for yielding to them. Immediately after; the Yak made a radio call that they too would be making a right 360 turn for spacing. It was at this point I decided the best course of action to avoid a collision would be to make a descending turn to the east and leave the airport environment. In doing so I descended to about 600 ft. MSL from the traffic pattern altitude of 868 ft. MSL and overflew some buildings at about 600 ft MSL. Once I heard the Yak was continuing in for landing I started climbing back to an appropriate altitude. We maneuvered back into the airport environment and landed without further issue.The problem arose by the Yak's non-standard pattern entry and decision to also perform a 360 degree turn in the pattern. Contributing factors: Our 152 is a high wing and the Yak is a low wing. The Yak may have associated our radio calls with a different aircraft in the pattern.