A teacher who sits in lounges and libraries doing nothing all day — sometimes even napping — is challenging the city to make him earn his $94,000 salary.

“I come to work every day, sit down and do nothing,” said David Suker, who spent 15 years helping “at risk” teens in the Bronx earn a general equivalency diploma, or GED.

Suker, 48, complains he is “warehoused” in the Absent Teacher Reserve, a pool of educators without permanent jobs that costs an estimated $100 million a year. Right now, there are 1,304 mothballed city Department of Education staffers in the ATR.

The DOE fired the Army veteran, who suffers from PTSD, after he made news as an Occupy Wall Street protester who clashed with cops. He appealed his firing in court and won, paying only a $7,000 fine.

But instead of returning Suker to his old job or a similar one, the DOE banished him to the ATR, where teachers, guidance counselors and others who can’t get rehired move from school to school as substitutes.

At least 200 educators who have been fined or suspended for misconduct or incompetence are currently stuck in the ATR.

The pool was meant for “excessed” teachers who lose jobs when their schools are downsized or closed, but it has become a dumping ground for those the DOE fails to fire in termination hearings.

Suker and others in the ATR say they mostly sit idle, substitute in subjects outside their expertise or do grunt work like lunch duty. The ATR staffers receive full pay and benefits.

At the Academy for Language and Technology in the Morris Heights section of the Bronx last week, Suker spent all day in a corner of the library but said the stress of being isolated got to him.

After a dispute with the principal’s secretary Wednesday, he was rushed by ambulance to a VA hospital for a panic attack. On Friday, he said, “I took a nap.”

Before being dumped into the ATR, Suker spent two years in a DOE “rubber room” — where he also napped — while awaiting disciplinary decisions.

Suker has filed a lawsuit in Manhattan Supreme Court that challenges the ATR system, contending the DOE has no right to impose this extra form of punishment on teachers.

“The DOE is not legally permitted to discipline tenured teachers without giving them the right to a hearing,” said Suker’s lawyer, Maria Chickedantz. She called the ATR a “drastic demotion” because teachers in it can’t earn overtime pay, and the label carries a stigma.

The DOE maintains it has the authority to assign teachers to the ATR after they have been found guilty of any misdeeds or ineptitude.

Judge Alice Schlesinger, who will decide the issue, rejected a similar complaint by Cindy Mauro and Alini Brito, teachers at James Madison High School in Brooklyn who were fired after getting caught trysting in a classroom. Schlesinger reinstated them but did not force the DOE to remove them from the ATR.

The DOE said it never sends teachers who escape the ax back to the school where they were charged. They can be rehired only if a principal agrees to do so.