The younger Mr. Rosales had been born into the margins of city life. At 15, his mother moved into foster care in the Bronx to escape her shame of her protruding belly. She raised Manuel there for his first months. At birth his chest was caved in at the sternum. Doctors told the family he might not make it to 30 without a heart attack.

Surgery at 13 masked the deformity, but his father said Manuel continued to be bullied at schools in Brentwood, N.Y., a Suffolk County town that is home to many Latino immigrants. Special education teachers called Manuel and his classmates “speds,” his father said. The family hired a lawyer to protest the administration’s attempts to have him home-schooled. But legal proceedings fizzled and Manuel dropped out around 17. (His father said he later earned a high school equivalency diploma.)

A spokesman for Brentwood schools did not respond to a phone message seeking comment on Sunday.

Mr. Rosales brooked no authority. And no targets were too senseless: His father said he destroyed a swimming pool and lit a fire on someone’s lawn. He spent two weeks at a psychiatric center on Long Island around 15 and began taking medication for bipolar disorder. “In the end I stopped that medication,” the elder Mr. Rosales said, “because he was like a kid that would stare at you, but not register.”

Mr. Rosales, who was 35 when he died, never again received treatment, his father said.

The Suffolk police arrested him 17 times from 1998 until this year, mostly on minor charges, but once in 2006 on felony assault charges. A county police spokesman did not have details of arrests or other encounters involving Mr. Rosales, but Mr. Rosales told a friend the assault charge was for getting into a fight with a police officer. He was imprisoned from 2006 to 2010, and again from 2012 to 2014 on a stolen property conviction. He later told friends he had once been in the Latin Kings gang.

On Sept. 23, 2013, with Mr. Rosales locked up in Downstate Correctional Facility in Fishkill, N.Y., his son was born.

“The first time I laid eyes on you I knew that I had to make a change in myself, I have to do better for YOU not for myself,” he wrote on Facebook on Antonio’s third birthday. “I promised myself that you would never have to wonder if your papa loves you, I’d give you what I didn’t have growing up.”