Flight Instructor reported an NMAC with another light aircraft in the pattern at 7S3.

Narrative

I was instructor pilot in right front seat. Student pilot was in left front seat. No other occupants.Airport's northbound runway was in use. We took off and climbed to 700 MSL (500 above airport elevation); then initiated left turn to crosswind; planning a left downwind departure which is standard procedure for this airport. We made radio calls taking the runway; turning crosswind; and turning downwind.We heard an aircraft coming in from the east; but standard protocol for this airport is to overfly the field at a minimum of 1700 MSL (1500 above airport elevation); fly at least 2-3 miles west so as to be well clear of the downwind area; then descend and teardrop back to the forty-five for the northbound runway.The approaching pilot said he was going to overfly the field and enter the downwind directly; not standard procedure for this airport unless the pilot is absolutely certain they are alone in the pattern; which usually only happens at night.We saw his ADS-B target; and it looked like he was doing as he broadcast. He either did not hear our radio calls and did not see us on his ADS-B display (if he had one); or he didn't care that he would be basically cutting us off on the downwind; just kept flying across the field and turned downwind with apparent disregard for us.We did not have Aircraft Y visually yet; so I assumed control of our aircraft from my student and initiated a steep right bank so as to raise the left wing. We still did not see Aircraft Y; but his target on our ADS-B display indicated he was far enough ahead for us to recover from the right bank and turn left to the proper downwind; although I made sure we remained at 900 MSL (pattern altitude is 1200 MSL) to ensure vertical separation and to increase our chances of seeing Aircraft Y.As soon as we leveled the wings on downwind; we saw Aircraft Y ahead of us. Estimated horizontal distance 200 feet. Apparent vertical separation per both ADS-B and visually was 200 feet.I captured the tail number of the Aircraft Y on my cell phone's Foreflight display; and when back on the ground I looked up Aircraft Y's flight path on website I also looked up our flight path on website and confirmed my narrative; above. I then sent screen shots of everything to our Chief Flight Instructor so he can look up the owner of the aircraft and contact the pilot; if he decides to do so; and inform him of the overflight and teardrop procedure described above.