CRJ-900 Captain reported encountering wake turbulence on approach to JFK 4 miles in trail of an A321.

Narrative

While on the RNAV (GPS) Z 13L between ASALT and CNRSE at 2;000 ft. in day VFR; we encountered what appeared to be severe wake turbulence resulting in a hard roll left and right. I said 'my aircraft' and attempted to disconnect the autopilot (though it may have disconnected itself). Immediately the rolling was stopped. Visually and on the TCAS display no nearby traffic was present however there was another aircraft ahead of us on the approach. Reporting the event to ATC we asked about traffic and they said it was an A321; which at that range; more than 4 miles; I thought was unlikely to produce wake three times stronger than any I have found in XX years. We checked the flight control and hydraulic synoptic pages and found all normal indications; and I found that hand flying was normal as well. We agreed that I would continue manual flight through the landing; which also was normal.So far as I understand; wake turbulence can be made stronger through many factors besides the originating aircraft's proximity and/or being slow; clean; and heavy. Things like relative wind; relative angle of the second aircraft to the wake; combinations of wake and the zone where the wind is shearing its speed or direction; and many other variables may combine to make it worse. I think in this case we were unlucky. I saw no issue with ATC spacing. I am not sure that such a rare event can reasonably be avoided but at the moment when it happened; the main concern I had was to get the autopilot off and to regain control of the aircraft without over-controlling of the rudder. The CRJ can recover from even more extreme wake but not if the tail suffers structural failure from over-control. I thought this might be a good lesson in the simulator. As I was now PF (Pilot Flying); and hand flying; I did not make a PA to settle passenger's nerves (as we would normally after a noticeable wake event) but I should have asked my FO (First Officer) to do so at some point. We both felt a little startled even until we parked at the gate.