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When Michael Cohen, President Trump’s former lawyer, was sentenced last month to three years in federal prison on fraud charges, he had the right to request any number of prison camps favored by white-collar offenders for their relatively resort-like settings.

But Mr. Cohen chose a shabby, low-slung building 75 miles northwest of New York City, with an antiquated weight room, an uneven tennis court and no swimming pool.

What the minimum-security camp at the Federal Correctional Institution in Otisville, N.Y., does offer is a rarity in the federal prison system: a full-time Hasidic chaplain who oversees a congregation of dozens of Jewish inmates who gather for prayer services three times a day.

“For a Jewish person, there is no place like Otisville,” said Earl Seth David, 54, a former inmate who attended kosher meals, religious classes and weekly Shabbat services in the prison shul, a shared space where the Torah scrolls are locked up every night.