The feds are probing whether workers at a city-run juvenile detention center sexually abused teenage inmates, The Post has learned.

Manhattan federal prosecutors have opened an investigation into the Horizon Juvenile Center in the Mott Haven section of the Bronx, which is operated by the Administration for Children’s Services, and have begun calling witnesses for interviews, sources said.

The federal probe focuses on allegations that ACS workers groomed Horizon juveniles to do their sexual bidding by promising them special treatment if they complied, such as the use of cellphones to make personal calls, sources told The Post. The workers allegedly would revoke the kids’ privileges if they resisted their twisted advances.

Former counselor Nathalie Medford, 46, has been accused of having inappropriate sexual relationships with at least three young male inmates, two of whom have since filed lawsuits against her, ACS and the city. All three of the victims were between 15 and 16 years old, the suits say.

Former Horizon inmate Franklin Maldonado claimed in his August lawsuit that Medford told him that if he “took care of her needs,” she would protect him from disciplinary action and give him special privileges such as use of her cellphone and the ability to watch “special” movies.

Former inmate Miguel Smith claims in his lawsuit, filed in May, that Medford got “jealous” when he started talking to female juvenile inmates and warned him that if he didn’t stop, “she would get her ‘crew’ to . . . make his life miserable at Horizon.”

When Smith finally cut Medford off in 2014, he was punished with false reports of misconduct, he claims in his suit.

Other counselors were sexually inappropriate, too, the former inmates have said.

Smith accused another Horizon worker of kissing him “in a sexually suggestive manner” and telling him to show her his genitals.

“If it was big enough, she would perform oral sex on him,” the worker told Smith, according to the documents in his lawsuit.

A third inmate was the subject of a 2015 Department of Investigation probe involving Medford.

According to a redacted copy of DOI’s report into the allegations that was obtained by The Post, Medford had “an inappropriate sexual relationship” with that resident.

DOI also found that Horizon workers failed to speak up about seeing Medford lying on the youngster’s bed “without her pants on” and hanging out in his room with the lights off, according to the report.

In 2015, DOI referred the matter for criminal prosecution by the Bronx DA’s Office, which then passed the probe on to Manhattan federal prosecutors earlier this year, sources said.

Medford’s lawyer, Daniel Walters, did not return requests for comment.

“We hope the feds will get to the bottom of this because the juveniles continue to be victimized by the city’s denial of these sexual assaults,” said Vik Pawar, the lawyer for Maldonado and Smith.

ACS referred The Post to the city Law Department, which declined to comment.