C172 pilot reported an NMAC on downwind to a non-towered airport.

Narrative

In summary; Aircraft Y cut above and in front of me on the downwind leg abeam the touchdown point. Chronologically; I was holding short Runway XX for Aircraft Z to reach ~500 feet on their departure upwind XX. Once clear; I called on CTAF with my intention to take XX and remain closed left traffic and began my roll onto the runway. Afterwards; I heard Aircraft Y call on CTAF 6 miles south; joining on the 45 downwind Runway XX. Aircraft A called as type aircraft 5 miles north joining left crosswind XX; with the departing traffic in sight. Aircraft Z called his southbound departure from the pattern as I climbed through approximately 300 feet.Anticipating traffic conflicts I called my crosswind turn and reiterated my intent to remain closed left traffic for XX and noted I did not have incoming traffic in sight; and requested the aircraft say type so I could understand if the traffic was slow or fast and if a high wing or low. I didn't hear a response. I called my turn downwind and arrested my ascent promptly at 1;650 feet MSL and chose not to accelerate to 105 KIAS as I feared not being able to see the traffic above my wing. I have ADSB-in; but the traffic was concentrated all together without distinction so I opted to keep scanning outside the aircraft.When I was abeam the 1;000 feet markers of Runway XX I spotted Aircraft Y at my 1:00 200 feet above and 400 feet horizontal turning left and descending. At this point I judged the airplane likely didn't have the capability to come in contact with my airplane and I maintained course. I do not recall the aircraft calling base. I called I would extend my downwind for the landing aircraft. Aircraft A called traffic on downwind in sight and that they would sequence behind me. I made a roughly 2 mile final without further incident. On the ground I met with members of my club assembling for our monthly meeting. One mentioned greeting the pilot as he was entering the terminal building; but he declined to chat.