COLUMBUS, Ohio—The owner of a local gun range called authorities last September, suspicious about an inexperienced group that had come to learn how to shoot a pistol. One of those men drew much wider attention last week.

Abdirahman Sheik Mohamud, a 23-year-old Ohio man back in town three months after he returned from training with violent extremists in Syria, was the leader of the group at the gun range, according to court documents from federal authorities. He was accused by federal officials in court papers of contemplating...