Cops discovered naked pictures of a student on the phone of a fired top Department of Education official busted for attempting to lure a 14-year-old to a hotel room with a hot tub for sex, prosecutors revealed Friday.

Police found the images on former DOE deputy chief of staff David Hay when they arrested him Sunday for attempting to entice an undercover cop posing as a 14-year-old boy in a Wisconsin town.

Prosecutors also disclosed how they stumbled upon the 39-year-old’s preying behavior in an 11-page filing in federal court in Wisconsin — a case that began when the now-former educator messaged a cop he believed was a teen named ‘Colton.’

The police investigator for the tiny town of Neenah, Wisconsin, listed his age as 18 on the dating app Grindr when Hay first messaged him in July 2019.

“Into daddies?” Hay asked.

“Colton” messaged back: “Maybe, r u into young guys. Im 14 not 18.”

“Yea I’m good w[ith] that,” Hay responded.

The pair exchanged messages for several months — many of them graphic — before finally planning to meet in late December.

Hay even booked a room at a local motel with a hot tub for the rendezvous before backing out at the last minute, saying his mother sustained an injury and the age difference gave him pause.

That was their last chat.

Cops nabbed Hay at Milwaukee Mitchell International Airport the day after that last exchange.

Investigators seized his phone and discovered years-old pictures of an apparently underage boy in sexually explicit poses.

Prosecutors reported the teen was identical to a student Hay had as the principal of Wisconsin’s Tomah High School, where he worked between 2011 and 2014.

Cops located the person — now of legal age — who said he sent “several photographs to David Hay in the past,” the papers show.

Prosecutors hit Hay with child pornography charge on Friday.

He already faced one count of using a computer to attempt to entice a minor with sex.

If convicted of enticement, he faces a mandatory minimum of 10 years behind bars with a possible life sentence. He also faces up to 10 years in prison if found guilty of possessing child porn.

Hay appeared Friday in court and did not enter a plea. Pending a Jan. 14 hearing, he was released but must stay in Wisconsin.

Hay’s attorney, Jonathan Smith, said he had an issue with “sufficiency of evidence” in the complaint.

City officials admitted this week that Hay was never fully vetted by the city’s Department of Investigation and blamed the failure on a massive backlog of 6,000 background checks that have plagued the office for years.

The DOE conducted two checks of Hay in 2016 and 2018. However, the DOE check is limited to just fingerprinting and criminal database searches and did not turn up any red flags, schools spokeswoman Miranda Barbot said.

DOI’s background check involves a more thorough scrubbing of a person’s financial history and background.

That lapse may have concealed holes in Hay’s resume.

The Milwaukee Journal Sentinel reported Thursday that Hay resigned from a Wisconsin school district in 2011.

Officials initially said the separation was mutual, but later revealed they discovered he used a district credit card for personal charges.

Before his arrest and firing this week, Hay made $168,000 annually as a top aide to Schools Chancellor Richard Carranza.

He was first hired in 2016 to work as a special assistant for then-chancellor Carmen Fariña.

Carranza promoted him to his inner circle in October 2018. Hay was sacked immediately after his arrest, the DOE said Monday.

“In my office, the chancellor’s office, I hold everyone, including myself, to a high standard,” Carranza said at an unrelated press conference Friday.

“We serve the children of New York City,” he added. “That’s why I immediately fired him.”