Air carrier pilot reported autopilot failure during initial climb. Flight crew returned to departure airport.

Narrative

I was the Captain on Flight XXXX ZZZ-ZZZ1 on Day 0. Our aircraft was an originator and the aircraft was powered up at the gate when I arrived. I reviewed the aircraft logbook and dispatch release and I performed the Cockpit Preparation Flows. There were no abnormalities with any of the preparation. The First Officer was the Pilot Flying and I then completed the preflight walk around and noted no discrepancies as well.During our taxi we successfully completed the Taxi Checklist with no abnormalities. Once airborne; at approximately 8;000 feet while hand flying; the First Officer mentioned to me that the flight controls felt stiff. We swapped aircraft controls and I noted that the Captain side also felt stiffer than normal and sluggish to control inputs. There were no control issues.We elected to put the autopilot on at around 10;000 feet. While on autopilot; the aircraft failed to intercept the lateral course programmed while in LNAV mode. A few moments later; while climbing; the autopilot failed. We received an AUTOPILOT FAIL" message. The higher the aircraft climbed; the more pronounced the issue became. I browsed all of the aircraft synoptic pages and noted no discrepancies on any of the systems. Due to the autopilot failure I hand flew the aircraft back into ZZZ. I had the First Officer; now Pilot Monitoring; [request priority handling] and change our destination back into ZZZ and load the arrival and obtain landing data.I swapped controls to the First Officer where I updated the flight attendants of the situation. I informed the customers of our return back to ZZZ as well.I came to a brief stop on the runway and we were able to taxi back to the gate under our own power without any further issues. Once at the gate I wrote a discrepancy in the aircraft logbook for aircraft flight control anomaly and autopilot failure."