TRACON Controller reported an aircraft losing its autopilot equipment and descending below the MVA.

Narrative

I was vectoring Aircraft X for a visual to ZZZ. I noticed them wandering from the assigned heading so I issued a turn. As I did that they responded they were having a problem with their autopilot. Very soon after it seemed they were losing control of the aircraft. They descended below the 030 MVA [Minimum Vectoring Altitude] and I issued a Low Altitude Alert. They responded they were a priority aircraft; with a malfunctioning autopilot. I turned on the EOVM [Emergency Obstruction Video Map] and I issued a heading to fly and altitude to maintain when able. I stopped departures at ZZZ1 as they were heading toward the departure corridor. I coordinated with ZZZ for the priority arrival. Aircraft X was able to get the aircraft under control eventually although they never climbed back to the MVA. I continued to issue vectors and eventually cleared them for an ODO [Opposite Direction Operations] arrival that was in line with their route to ZZZ. I was only able to get the minimum information available as the event was extremely time-critical and the pilot was nearly overwhelmed just trying to maintain control of the aircraft.