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In the mid-1970s, students at one of New York’s most esteemed prep schools were surprised to encounter a new teacher who pushed the limits on the school’s strict dress code, wandering the halls in a fur coat, gold chains and an open shirt that exposed his chest.

The teacher, Jeffrey Epstein, would decades later face allegations that he coerced and trafficked teenagers for sex. At the Dalton School on the Upper East Side, some students saw Mr. Epstein as an unusual and unsettling figure, willing to violate the norms in his encounters with girls.

Eight former students who attended the prestigious school during Mr. Epstein’s short tenure there said that his conduct with teenage girls had left an impression that had lingered for decades. One former student recalled him showing up at a party where students were drinking, while most remembered his persistent attention on the girls in hallways and classrooms.

“I can remember thinking at the time, ‘This is wrong,’” said Scott Spizer, who graduated from Dalton in 1976.