Flight Instructor reported a near midair collision with a UAS while they were on final approach. The reporter took evasive action and reported the encounter to ATC.

Narrative

I was acting as PIC of Aircraft X. The flight mission was a discovery flight w/ intro to control tower ops with Person A. I was flying north from ZZZ to DAY. I obtained the ATIS information and contacted Columbus Approach to obtain flight following into DAY airspace. Approach routed me to the left-downwind leg of 24L and frequency changed me to 119.9 DAY Tower. DAY gave orders to continue extended downwind leg until told to turn base. Approximately 3-5 nautical miles distance from ZZZ we; Aircraft X; received clearance to 'return for the option'; to which we immediately complied. Approximately 2 nautical miles on final approach; at ~1;800 ft. MSL (~800 ft. AGL); I noticed a large 6-Armed Hex-Copter Drone. It was straight ahead on long final; at altitude; and was silver and red. I took evasive action of steep turn to the left for a few seconds and then steep turn back to the right so not to trail off course too much. We came within ~200 ft. horizontal distance. I contacted DAY Tower immediately so any following aircraft would be advised of the drone on glide slope on final for 24L. Did my touch and go and started my departing procedures. Dayton Tower asked a couple questions like the size; location of near-miss; and color-scheme of the said drone to which I advised them of the knowledge that I knew about. Then they switched me over to Columbus Departure. Departure then informed me that DAY Tower had some more questions and wanted to give me a phone number. I received the phone number. Approximately ~8 nautical miles from ZZZ; I informed Departure that I had ZZZ in sight and they cancelled flight following. After landing and shutting down and securing the aircraft; I called the phone number given to me by Departure. Over the phone; the tower controller; Person B; informed me that he was glad that I informed him of the drone because he had to divert 2 airliners to another runway so they would avoid the risk of collision with the drone and requested that I fill out a report to which this is the said report. Also; talked to local authorities and told them the same report; location; et cetera; the same information that I gave to DAY Tower. To which the local authority representative said that it was a little beyond his wheelhouse/jurisdiction and said that another government authority would be in contact soon and would want a report. Within the next 15 minutes the other government authority; Person C; asked about the same information as above; and so; I reported the same as before.