Two Long Island men are among four veteran correction officers convicted in Bronx Supreme Court this week in connection with the March 2013 assault on an inmate in the Rikers Island jail, authorities said.

Christopher Huggins, 34, of Westbury was convicted Thursday of second-degree assault and first-degree offering a false instrument for filing, a day after Michael Dorsainvil, 40, of Valley Stream, was convicted of second-degree assault and first-degree falsifying business records.

A Bronx man, Ronald Donnelley, 63, was also convicted Thursday of first-degree offering a false instrument for filing and a Queens man, Mark Anglin, 41, was convicted of the same charge a day earlier.

All four officers were convicted during bench and jury trials presided over by Judge Michael Gross.

Officials said the men took part in or helped cover up the assault on an inmate at the George Motchan Detention Center, an incident that was at least partially captured by video surveillance.

“These verdicts send a strong message to the city’s correction officers: engage in brutal behavior, lie to cover it up and you will be punished,” said New York City Department of Investigation Commissioner Mark G. Peters. “The defendants in this case are just four of the 33 corrections staff DOI has already arrested as part of its crackdown on lawlessness at Rikers. DOI’s investigation continues.”

They are scheduled to be sentenced on Dec. 7.

Some of the men’s attorneys could not be reached for comment, but Huggins’ lawyer, Frank Rothman of Manhattan, said he was relieved his client was not convicted of the top charge at indictment, first-degree attempted gang assault.

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“It was obvious from the video evidence that there was going to be a conviction of some level of crime,” he said. “The question was whether we could beat the top count. . . . I understand the judge’s decision.”

Rothman added that his client is now subject to a range of sanctions ranging from no jail time to up to 7 years in prison. Had he been convicted of the top charge, Huggins would be required to serve at least several years in prison, Rothman said.

Dorsainvil’s attorney, Peter Troxler of Manhattan, said, “I think Mr. Dorsainvil is obviously disappointed with the verdict and we are evaluating any and all steps to be taken both before and after the sentencing in December.”

Officials said the March 15 incident began when Dorsainvil and Huggins entered a holding cell and Dorsainvil struck the inmate in the face, causing bruising to his mouth that was treated with stitches.

Officials said the men, along with Anglin, filed false use-of-force reports saying the force was necessary to prevent the inmate from committing suicide by hanging. Donnelley, officials said, filed a report stating he was a witness to the attempt to save the inmate — but the investigation and evidence presented at trial revealed the videotape did not corroborate the men’s version of the event.