A sex offender with a lengthy rap sheet was arrested in Virginia for the murder of a Queens teenager after cold case detectives found DNA evidence under the victim’s fingernails that linked him to the killing, officials said Tuesday.

Jerry Lewis, 58, of Shawsville, Virginia, was arraigned Monday for the May 7, 1992 killing of 15-year-old Nadine Slade, who was found naked and strangled with her own bra inside the bathroom of her family’s Far Rockaway home, Queens District Attorney Melinda Katz said in a statement.

Lewis is a career criminal who served six years in prison after he was convicted in 2015 of breaking into an 88-year-old woman’s home in Queens and sodomizing her at knifepoint, according to prison records.

Detectives told The Post they broke open the fossilized cold case by requesting DNA testing on preserved fingernails clipped from the girl’s body.

“We were just digging through old homicide cases and saw that [the Slade murder] had some forensic possibilities,” Det. Donnamarie Mazza of the city’s cold case squad told The Post.

The results matched Lewis’s DNA, Mazza said.

So she traveled to southwestern Virginia to interview him. Lewis was about to be picked up for a parole violation — police in the Old Dominion had twice arrested him for allegedly beating his live-in girlfriend, Mazza said.

Still, he spoke freely to the New York City detective for nearly four hours, she said.

He fought extradition, but authorities eventually brought him to the Big Apple on April 28, where he was charged.

Queens Supreme Court Justice Kenneth Holder ordered Lewis to return to court on June 7, the release said. If convicted of the second-degree murder charge, he could be imprisoned for 25 years to life.

He is being held at the Eric M. Taylor Center on Rikers Island, records show.

“Any mother’s worst nightmare is to survive a child,” Katz, the district attorney, said in a statement. “To lose a child in such a horrific way causes unimaginable pain. Not knowing who committed the crime compounds the suffering.”

“In the end, we hope to achieve justice for Nadine and bring closure and some measure of solace to her bereaved mother.”

Mazza might agree.

“Her mom says she hasn’t slept through the night in 31 years,” the detective said. “Their lives don’t go on — they are still stuck in that day.”