The city’s embattled Housing Authority has suspended a third employee — a supervisor — at the Bronx housing project rocked by salacious allegations of on-the-clock orgies, officials confirmed Thursday.

Officials said the Throggs Neck Houses resident building superintendent, Wallace Vereen, was sent home without pay for 30 days as authorities continue to probe allegations of misbehavior by staff at the development, but would not confirm if he was linked to the sex party complaints.

“It’s a broad probe,” said one official.

That’s one of at least two investigations launched into the project and its staff. The Department of Investigation reversed course last week and started its own probe after it previously forwarded the complaints to the authority.

The Housing Authority previously suspended two employees after The Post reported that no workers had been reprimanded as the investigation continued. One of those employees was Brianne Pawson, the daughter of NYCHA executive Charles Pawson.

Both have declined to comment.

The suspensions come after the entire staff of the Throggs Neck Houses — roughly 40 employees — was reassigned to other developments around the city.

NYCHA officials first learned of the sex party allegations in May and DOI referred complaints it received to NYCHA in August. The massive staff reassignment followed shortly afterward.

Residents at the development said allegations swirled for months about mismanagement and Vereen playing favorites with staff — after the authority’s months-long failure to fill the development manager position left him effectively in charge.

“I’m coming from the angle of mismanagement of funds, I’m coming from the angle about bullying of staff,” said Monique Johnson, who leads the tenant association. “That’s why he got suspended.”

Johnson also described allegations of rampant favor-trading between Vereen and his staff but said she did not believe he participated in Pawson’s alleged on-the-clock sex parties.

“Whoever was his flavor of the month got special treatment,” said Johnson added. “He had his own thing going on.”