The August fight was sparked by a fellow inmate asking Patterson about his crimes, a release from the department said.
In the video released Thursday, Patterson can be seen speaking with another inmate before the inmate puts his hands up and moves toward Patterson. Patterson then punches the other inmate and the two begin wrestling.
The fight ends when a corrections officer fires a beanbag round at the men, striking a rail in front of them.
In the video you can see Patterson and the inmate stop fighting and lay on the ground following the discharge of the beanbag.
When questioned, Patterson told an officer that he was approached by two inmates, including the one he later fought with, regarding "his case involving a 14-year-old girl," according to the release.
Patterson said the inmates told him to leave the gym because of his crimes, the release said.
Neither inmate was seriously injured and both were put in prehearing detention pending the outcome of the disciplinary process, according to an incident report.
CNN has been unable to reach Patterson's public defender during his trial in Wisconsin, and it is unclear when or why Patterson was transferred to a prison in New Mexico.
