Theophilus Samuel was already at work when the call arrived.

Monday morning had begun like any other. Mr. Samuel, 55, had commuted to his job at Zucker Hillside Hospital in Queens, where he changes linens and prepares rooms for patients.

It was still early when his phone lit up with a call from his daughter and a son. Their voices were urgent: Sanjay, Mr. Samuel’s 13-year-old, had been shot while he was walking to school in the Cambria Heights section of Queens.

Mr. Samuel left work and ran to Cohen Children’s Medical Center, where his youngest boy lay in a bed, surrounded by doctors, in the emergency room. Sanjay Samuel had been struck in the back of the head, his father soon learned. The boy’s brain was swelling, and he had suffered extensive tissue damage. His chance of survival was slim.

On Wednesday afternoon, after spending two days on life support in the intensive care unit, Sanjay was pronounced dead, having lost all brain activity, according to Mr. Samuel and the police.

Joseph Kenny, the chief of detectives at the Police Department, said in a Tuesday briefing that the shooting had been gang related and that it had been sparked by a fight between Sanjay and a 16-year-old boy that the police had identified as a possible shooter.

The police on Thursday were searching for the boy, who lives near the scene of the shooting and is known to be a “troublemaker in the area,” Chief Kenny said. Sanjay was not in the police’s criminal gang database, nor did he have a criminal record, he said.

The death, which follows a spate of shootings this summer that have involved teenagers, has horrified residents and left the Samuel family heartbroken.

“The last few days, it’s just been really hard,” Mr. Samuel said in an interview on Thursday, pausing briefly to collect himself. “It’s very difficult as a parent.”

According to Mr. Samuel, on Monday morning, Sanjay had been on his way to his high school on Hillside Avenue, where he was in the ninth grade. He had stopped with a group of boys outside a Dunkin’ in a strip mall on Linden Boulevard.

Just after 8 a.m., the 16-year-old rode up to the Dunkin’ parking lot on a scooter and confronted the group, according to Chief Kenny. Yelling ensued and then the boy pulled out a gun, sending the others scattering, he said. The boy then mounted his scooter and turned to leave, but before he could, the fighting began anew and he and Sanjay began to punch one another. The boy then shot Sanjay once in the head and fled, Chief Kenny said.

Nazmina Poly, the manager of the doughnut shop, said she had been working in a walk-in freezer when she heard a commotion. When she came outside, she saw the body of a young boy lying on the concrete in the parking lot and a few children standing around him.

Police officers and emergency medical workers responded to 911 calls and took Sanjay to Cohen Children’s Medical Center in critical condition, the police said. He was placed on life support soon after he arrived, Mr. Samuel said.

For the next two days, Sanjay’s father, mother and a stream of relatives camped out at the hospital, waiting by his bed while a machine breathed for him. A test on Tuesday showed that Sanjay no longer had brain activity, Mr. Samuel said, but doctors pressed on.

His condition worsened, his face began to swell and on Wednesday afternoon, after another slate of tests, doctors pronounced Sanjay dead, Mr. Samuel said.

The shooting on Monday is the latest is a string of killings in New York City in recent months involving teenagers. In June, Darrell Harris, 17, was shot during a water gun fight in a Bronx park. The next day, Jamuri Mezar, 14, was killed after being struck in the head by a bullet inside his Queens apartment. A 15-year-old boy was charged with second-degree manslaughter in connection with the death.

On Thursday, Sanjay’s family remembered him as a jovial boy who had loved fishing, basketball and listening to reggae music.

Standing outside the Queens home where they grew up, Steffon Gordon, Sanjay’s 30-year-old half brother, said he had always tried to act as a role model. Mr. Gordon said Sanjay often came to him for advice, but that recently he had been trying to respect the boy’s privacy.

“That was my biggest mistake — not being more in my brother’s life,” Mr. Gordon said. “My brother lost his life in the streets as a 13-year-old. That is not normal.”

Mr. Gordon did not say whether his younger sibling had been involved in gangs, but said it had at times been challenging to keep him insulated from bad influences.

“Being a kid, you just make mistakes,” he said. “Maybe you got suspended from school. Maybe you came home 10 minutes late. That’s a kid mistake, that’s a 13-year-old mistake. This right here, this is grown people business.”

Taylor Robinson and Maria Cramer contributed reporting. Sheelagh McNeill contributed research.