C172 pilot reported an NMAC due communication issues with the aircraft.

Narrative

I was on a direct flight path from ZZZ1 to ZZZ and confirmed with ZZZ Approach that I was approved to changed frequencies to ZZZ. Once I was approved to changed frequencies I began calling out my position to the CTAF for my positions at 10; 5; and 3 miles outside of the airfield.I then let the traffic know I was entering the right downwind for Runway XX and saw a plane exiting the runway on the ground; but no other traffic in front of me. When I announced I was turning base I heard another call that that someone was going to extend their downwind; but still did not see any traffic in front or around me. I had thought this was to allow for my approach. After I called that I was turning final I was in line with the runway; I heard another call that someone was turning base. I was a little high; but nothing to cause concern so I went a little further down the runway than normal.When I landed I heard someone talking about Aircraft X on the radio asking if they didn't see the other plane. When I said that I was flying Aircraft X and asked details about what just happened; I didn't get an answer. When I exited the runway I saw another plane exiting very early on in the runway and realized that we must have come down at the same time. When I parked and spoke with the other pilot; I was apparently coming down directly above him. Thankfully he was making a short field landing and I was a little long for mine or things could have been a lot worse.There were multiple things that seemed to be going on at the time of this situation.Nobody was picking up my communications and they thought that I just came out of nowhere; even though I could hear everyone else. They were also checking the other ADS-B in the area and he said that I was nowhere to be seen on there.After getting inside we tracked my ADS-B and it showed my travel from ZZZ1 to ZZZ; but it dropped the signal about a mile from ZZZ.I checked my comms when I was leaving ZZZ and confirmed that I was heard loud and clear before I left. I'm not sure why I had communication with ZZZ1 Ground; ZZZ1 Tower; ZZZ Departure; and ZZZ Approach; but then nobody could hear me when I switched frequencies to ZZZ.In the future I will ensure to have 2 way communications with other pilots in the pattern of a non-towered airport to make sure that they are hearing me properly.