An ugly antisemitic incident in the tony Scarsdale School District has sparked an internal probe — and even entangled the kid of a school-board member.

The disturbing situation occurred when flyers posted by the posh public high school’s Israel Culture Club to promote an upcoming “Israelfest” were ripped off the walls and dumped into boys’ bathroom urinals — with images of the vandalism quickly making the rounds online.

That’s when the 17-year-old daughter of school-board member James Dugan stuck her nose in. 

“Keep up the good work,” she wrote on Instagram next to a photo of one flyer inside a urinal and four fire emojis. 

The glib online comment did not sit well with parents in the suburban Westchester County district — one of the country’s wealthiest and highest-rated public-school systems — and forced both dad and daughter to apologize for the slip.

“I foolishly posted that angry, obnoxious meme about Scarsdale High School,” the girl said in a statement to The Post. “Realizing my mistake, I quickly took it down because I know it was offensive and inappropriate and I wish I had never posted it.

“Nothing about that represents my values or those of my family,” the teen said. “I’m sorry I did it and have learned a real lesson from the response.”

Dugan addressed the issue in his own letter to parents. 

“Recent events have provided a profound teaching moment for me as a parent and have impacted me and my family,” he wrote. “As a parent I will focus on healing my family.

“But as a school board member, my focus will continue to be on our students, our schools, and our education program.”

In a letter to district parents, Scarsdale High School Principal Kenneth Bonamo said the Israeli club’s flyers were torn off walls, with many hurled into boy’s room urinals, while an Instagram post promoting Israelfest prompted “vulgar” comments, including by a non-student.

“These behaviors are unacceptable and more broadly should be disturbing to the entire school community for the intolerance they represent,” Bonamo wrote. “Please be assured that we take these concerns to heart as we work to uphold our standards of conduct and community values.”

He said some in the New York school community complained that the map of Israel on the club’s flyer included “disputed territories as part of the State of Israel” but said that was no excuse for the vandalism.

“This is a core conflict in this debate, one that is worthy of exploration in civil discourse,” Bonamo said. “But responding in this way is still no appropriate.”

Scarsdale Superintendent of Schools Drew Patrick addressed the incident in a separate letter to parents.

“We live in a time of rising antisemitism, political polarization and a degraded civil discourse,” Patrick said. “I want the community to know that we take these complex challenged seriously and work to confront them every single day.”