PA-44 pilot reported an NMAC during final approach requiring a minor evasive maneuver to avoid a possible collision.

Narrative

I was #2 on the 45 deg pattern entry for Runway XX in the PA24 and had visual and radio contact with the C150 ahead of me and approx half a mile separation as we were both slowing into pattern speed - we had both been coming in from the north and I had a slow rate of closure from about a mile to half mile over 3 or 4 minutes. I had reduced engine power and was slowing to my preferred gear extension speed of 110 mph and glanced down for a second or so to check my airspeed decay rate prior to extending the gear and turn the fuel pump on as part of my pattern entry checklist; and when I looked back up the C150 was much closer than it had been. I initiated a minor evasive maneuver (climb and diverging right hand offset to ensure clearance) at approximately the same time the C150 pilot called that he wanted me to go in front since I had a faster pattern and landing speed. The remainder of the approach and landing was uneventful for both aircraft.Once on the ground we had a friendly (actually; it was very friendly; no egos on either side) debrief of the incident and the C150 pilot had me on ADS-B in and anticipated I would overtake prior to initiating the 45 entry; and so when I hadn't he had kept power up but as we got closer to entering the pattern he became uncomfortable being at a faster speed than he was used to and pulled back on the power and put in some flaps; apparently just before I glanced down at my panel; with the result that his configuration changes essentially put the brakes on while I wasn't looking.Overall there was still enough room to adjust and clear without requiring excessive control inputs; but it did catch both of our attention as an incident to learn from - for me; half a mile is too short a distance to be following an airplane that can slow down quickly into a pattern and for him it was to be a bit more communicative when he wants a trailing airplane to overtake.