The city is waging an all-out battle to overrule a judge who refused to let it fire a junkie teacher — who reported for jury duty carrying a stash of heroin.

Damian Esteban was nabbed in 2012 for bringing 20 bags of heroin through the metal detector of a Manhattan courthouse, an act that turned the school system into a national laughingstock, according to an appellate-court brief filed by city lawyer Deborah Brenner.

“Parents who send their children to public schools under compulsory education laws have a right to expect educators who are not foolish in the extreme and do not handle dangerous drugs with reckless abandon,” the brief reads.

Public-school teachers must have “at least a minimal level of intelligence and good judgment,” Brenner added, quoting an arbitrator’s original decision to fire the former teacher at the Williamsburg HS for Architecture and Design.

The 36-year-old teacher — who admitted during an administrative hearing that he walked into a courthouse “full of police officers and prosecutors” without realizing that he had the 20 glassine packets in his pocket — won a lawsuit to get his job back in September 2013.

He has not yet returned to teaching, pending the outcome of the appeals process.

In its argument, the city Law Department says there’s more at stake than one teacher’s job — like the reputation of the country’s largest school district.

Esteban’s “misconduct had held DOE up to ridicule in local, national and worldwide media,” Brenner’s papers said — adding that the Department of Education “must have the prerogative to terminate a teacher who was legitimately characterized as a ‘jury-duty dope’ and a ‘junkie high-school teacher’ in the press.”

The Brooklyn school where Esteban taught for five years before getting arrested has had trouble recruiting students since, according to officials.

Brenner blames Manhattan Supreme Court Justice Manuel Mendez for buying Esteban’s excuse that the addict was only using on the weekends and forgot he left the drugs in a little-used backpack.

Esteban had actually stashed them in a cigarette box plainly visible in his pants pocket.

His lawyer, Eugene Eisner, said he has a new career — he’s writing a book about the debacle.

“I think it will be a best seller,” Eisner said. “It’s a very interesting case.”

Esteban said he started using painkillers after he broke his leg and then got addicted to heroin. He maintains that he’s kicked the habit.

Eisner boasted of his client’s “sterling record as a teacher.”

But Brenner counters in court papers that Esteban’s tenure was “brief and undistinguished.”

The social-studies and Spanish teacher had been given two “unsatisfactory” ratings during his career.

One came after a supervisor noted that students treated his classroom like a waiting area, reading newspapers, coming and going at will and carrying on loud conversations.

In the other instance, the principal found Esteban used class time to write lesson plans while “students were supposed to be working on an in-class assignment . . . many of them did not even have their books open.”

Eisner said he’s confident Esteban will win the appeal.

If he prevails, Esteban will ask the court to award back pay, he said.