GA pilot reported Alternator Failure in cruise. Smoke was coming from the panel; so the flight crew turned the Alternator switch to off and turned back to the departure airport while requesting priority handling. The flight crew made a precautionary landing and shut down to evacuate on the runway.

Narrative

Aircraft X departed ZZZ to the northwest; headed to ZZZ1 to practice landings for a training flight. We requested an on course turn and it was approved around 1800 ft. MSL. We then flew on a heading of roughly 340 while climbing to 3500 ft. MSL. We were in cruise for roughly 3-5 minutes before receiving an Aural Annunciator. This Annunciator was accompanied with the amount of Volts in the Battery displaying Red (usually White); and the Alternator Amps reading 0. I immediately then assumed an Alternator Failure; and told Person A to open up the Alternator Failure checklist. Almost immediately after Person A grabbed the checklist; smoke started to come from the left and under the Primary Flight Display (PFD). I immediately opened the storm window; [requested priority handling] with ATC; then turned the Alternator Switch OFF. We turned right to enter an extended final for Runway XXR. I then turned off all other unnecessary electrical equipment. ATC asked us to get In front of traffic that I believe was on a VOR approach; and we did. After telling Approach we had the traffic in sight; we got switched over to Tower. Upon switching to Tower; I informed them of our situation and they cleared us to land XXR. I informed ATC that once I turned the Alternator off; the smoke seemed to stop. After some discussion with Tower; and brief thinking with myself; I informed Tower I intended to shut down on the runway. I flew a fast approach in hopes to get on the ground sooner than normal approach speed. We landed on Runway XXR; and I immediately informed ATC we stopped and were going to shut down. Person A and I evacuated the aircraft after shutting down; and departed the runway in an airport vehicle. Alternator wiring issue. Once turning the alternator switch off (post-smoke); the smoke seemed to go away. In the event of smoke in the cockpit; I would take the same course of action.