Light transport pilot reported that during landing rollout the aircraft began to drift off centerline and did not respond to rudder inputs. The pilot used differential braking to steer the aircraft back onto centerline and exit the runway safely.

Narrative

We picked up Aircraft X in ZZZ1 for an empty reposition flight to ZZZ. Aircraft X had recently been worked on for a write up concerning 'no nose-wheel steering.' This write up had been cleared by Maintenance and the aircraft had been returned to service. While taxiing out at ZZZ1; I made sure to test all functionality of the nose-wheel steering components (rudders and tiller operation) as well the NWS disconnect function on the yoke. Everything seemed to be working fine so we departed ZZZ1 for ZZZ. We made a visual approach backed up by the RNAV XX to Runway XX. Winds were gusting 80 degrees from the right at around 15-18 kts. We made an uneventful; crosswind landing on Runway XX and after lowering the nose to the ground I deployed the thrust reversers and began braking shortly after. Because of the right crosswind; I was still holding in right aileron control when I noticed the aircraft was staring to drift left across the runway centerline. I tried putting in right rudder to counteract the drift and received no response from the airplane. At this point we had slowed down to about 80 kts. and I grabbed the tiller and tried to put in right tiller to steer the aircraft back to centerline and found I had no steering control using the tiller either. I began modulating the brake pedals and used differential braking to steer the aircraft back onto centerline while we continued to slow down. Once I knew we had the aircraft at a taxi speed and we were nearing the end of the runway; I elected to use the brakes to steer the aircraft slowly off the runway and onto the taxi way at the intersection of Runway XX and Taxiway XX. The ramp is right there on Taxiway XX so I steered straight ahead and slowly worked the airplane onto the ramp and clear of the taxiway as to not be an obstacle for other aircraft operations. We set the brake and shut the aircraft down once we knew we were out of the way and in a safe position. No damage to aircraft/persons/property occurred.