B737 First Officer reported the aircraft was restricted to only making left turns due to a malfunction with the flight controls to the right. The flight crew performed an air turnback and as the aircraft slowed down after touchdown; the aircraft wanted to veer to the right. The First Officer stated that this was the third flight with this issue.

Narrative

The Captain was flying this leg. It was a normal takeoff. After 400 to 500 ft. AGL; we started our right turn to 025 degrees as per the departure procedures are required. During the turn; we were told to contact Departure. As I contacted Departure; they gave us a right turn direct to our next fix. Captain said that the plane wasn't flying right and said we are leveling off at 5000 ft. and remaining on current heading. He then told me to [request priority handling with ATC] and a return to field. He told me that the controls were snapping fully to the right and it was very hard to return the aileron position back to neutral. He then stated that banking the controls to the left was normal but banking it back to the right would snap the ailerons fully to the right again. We told Departure that we could only make left-hand turns and requested to return to the field for Runway XXC.We then continued to shallowly bank the plane to the left to avoid large control inputs that would cause snapping of the ailerons. Captain mentioned that he was holding the controls with extreme force. As he was flying; I set the plane up for the ILS XXC. I proceeded to look for a flight control QRH regarding the ailerons. I then gave the FAs (Flight Attendant) a call to let them know the situation and that we are landing in about 10 minutes. I then made a PA to the passengers that we had an indication that we needed to return to the airport. We lined up with [Runway] XXC and the Captain noticed as I extended flaps; he felt binding and snapping of the controls. We had an overweight landing with a smooth touchdown about 200 FPM. As the airplane slowed to around 10l kt.; we both noticed the airplane wanting to veer to the right. The Captain applied pressure to correct for it. We exited the runway and taxied safely to the gate.Flight control issues with right deflections. This was the third flight with this issue. Maintenance needs to do a thorough inspection on the aircraft and test fly to make sure it is good for operation.