B737-800 Captain reported encountering wake turbulence on approach to JFK in trail of a B757.

Narrative

We were established on the RNAV [Runway] 13L for JFK; fully configured. I was PM (Pilot Monitoring) and did not have the traffic ahead of us in sight. Shortly after crossing CNRSE; with the autopilot on; we hit the wake turbulence from the aircraft we were following. It rolled us violently; gave us a roll alert on the PFD and put the autopilot into CWS. I immediately asked who we were following and was told a 757. The autopilot was no longer following the RNAV course and descent profile. My FO (First Officer) clicked off the AP and FD and began correcting the course and path; the path was very challenging because of the crosswind and the continued rumbles of wake turbulence from the aircraft we were following. We ended up slightly high going through 1;000 ft.; but we were in a position to safely land. We did have a brief high descent rate caused by a wind gust and my FO correcting. We landed safely in the touchdown zone and taxied to the gate uneventfully. With all that being said I should have called the go around early; when we realized how badly the wake turbulence had [affected] our path. I allowed myself to be caught up in the 'we can fix it' mind set; which was wrong. The next time I run into a situation similar to this we will go around.Having a better idea of what aircraft you're following so you can try and predict wake turbulence. Not trying to fix a bad situation on final. Just go around and shoot the approach again.