B737 Captain reported they had rudder issues during takeoff roll resulting in a rejected takeoff.

Narrative

I handed controls to the FO and he initiated the takeoff roll. After setting power and hitting toga; he noticed that the airplane required full right rudder and was still moving left of centerline. He stated that his rudder was not working. I called for the reject and took controls at 50 kts. When I took controls; the left rudder was fully depressed; but when I pulled the throttles back; the airplane seemed to be fully controllable and the abort was uneventful.We exited the runway and stopped the aircraft. We called maintenance and they told us to return to the gate. They ran all the checks that they could to test the controls; and found nothing abnormal. Maintenance said that in order for it to be released back into service; they needed us to taxi the airplane and check control surface movement. We did this and everything seemed normal. We returned to the gate again and the aircraft was released to us again. We loaded passengers and departed the gate. I told the FO that I would prefer to fly the plane for this leg and we agreed that that was the best option. We flew back to ZZZ without incident.