Socata Trinidad instructor pilot reported a rough running engine after performing a touch-and-go landing; resulting in an immediate return to the departure airport.

Narrative

While conducting a local area flight to validate the autopilot functions on a Socata Trinidad aircraft; we entered the traffic pattern at ZZZ Airport to perform a touch and go landing prior to returning to the aircraft home base at ZZZ1 Airport. The landing at ZZZ was normal but as power was applied for the touch and go the engine vibrated slightly and began to run rough. We immediately aborted the takeoff; advised the tower and cleared the runway. We requested to taxi to a holding pad at the base of the tower to evaluate the aircraft. We performed a magneto check and noted the left magneto was running rough. We performed a run-up and leaned the fuel mixture to burn off any lead deposits fouling the spark plugs. After another magneto check the engine was operating smoothly. We departed ZZZ for the short flight back to ZZZ1 only a few miles away. While descending to pattern altitude at ZZZ1 the engine started to run rough again. We were on an extended downwind following another aircraft in the traffic pattern. We [requested priority handling] with ZZZ1 Tower and requested an immediate left base turn toward the runway. ZZZ1 Tower cleared us to land. We advised that we did not require crash-fire-rescue support and landed the aircraft and taxied clear of the runway. We returned the aircraft to the hanger and performed another magneto check and noted roughness on the left magneto. We have scheduled the mechanic to evaluate the magnetos and perform any necessary repairs.