The city is facing a lawsuit from a mom who claims a teacher had a sexual relationship with her son — and that everyone at Manhattan’s Hunter Science High School knew about it.

The mom claims Margaret Ann Riordan, 31, allegedly introduced the youth to “sexual positions, self-hatred, depression and suicide,” the teen’s mother claims in her Manhattan Supreme Court legal papers filed Thursday.

Riordan was a history teacher at Manhattan Hunter Science HS in Lincoln Square when she met the male student and began having sex with him in 2010, the mother alleges.

Riordan continued to contact him until her arrest on Sept. 26, 2011, when an officer caught her kissing the boy at a Roosevelt Island park, according to a criminal complaint filed in the case.

The teacher was charged with a misdemeanor for endangering the welfare of a child and third-degree sexual abuse — but took a plea deal in January and was sentenced to 10 days community service.

Riordan eventually resigned in January, said Department of Education spokeswoman Margie Feinberg, who declined to comment on the lawsuit.