The 13-year-old boy gunned down outside a Queens Dunkin’ Donuts this week was slain over a gang beef, police claimed Thursday — as they identified a fellow teenager as the suspected killer.

Cops believe the still-at-large suspect — 16-year-old Campus Magnet High School student Jaysohn Sykes — allegedly rolled up on a Razor scooter and shot young Sanjay Samuel in the head outside the coffee shop at around 8:20 a.m. on Monday, leaving him brain dead, NYPD Chief of Detectives Joseph Kenny said.

Samuel, who attended Martin Van Buren High School, was not affiliated with a gang, his family said, despite the NYPD noting he would post on social media about the SSM, or Sex Money Murder, a subset of the Bloods.

“Trust me, I don’t know anything about such activities, talking about gang activities,” the boy’s grieving dad, Theophilus Samuel, told The Post.

“He wasn’t involved in nothing. Every time I called him when he should be home from school, he was home. I have a tracking device on my phone so I could track him,” the father added.

The slain teen – who identified himself as “J2 Guns” on Instagram – was not listed in the NYPD’s “criminal group database” and had no criminal history, the police official said.

“He posts quite frequently – SSM with a drop of blood,” Kenny told reporters.

Samuel’s mother blamed the horrifying shooting on the minor’s cell phone and social media, on which he would post things to “look grown.”

“This phone is a devil,” Velene Griffith told The Post. “These kids — they talk too much on social media. They live on the phone, on social media to hype themselves up, to look grown, to look big and bad.”

Investigators believe the alleged gunman, Sykes — who goes by the name “Flex” — shot Samuel during a group brawl, Kenny said.

“He walks up to the group and confronts them. They’re yelling back and forth. Suddenly, the group scatters,” Kenny described.

“We believe at this point, our perpetrator pulls out and displays a pistol, which causes the crowd to disperse a little bit,” he continued.

“The perpetrator gets back on the scooter to leave. The crowd starts yelling at him again. He comes back, at which point he gets into a physical fight with our victim,” Kenny said.

“They start throwing punches at each other, and then a shot is fired. He goes down. Our perpetrator flees the scene.”

A good Samaritan spotted Sykes fleeing and tried to stop him — pleading with the teen to surrender and hand over his gun — but he refused, according to Kenny.

Instead, Sykes brazenly asked the do-gooder for a ride, the chief said.

“Obviously, the civilian says no, but says, ‘Can I have your sweatshirt?’” Kenny said. “And for some reason, the perp gives him his sweatshirt. So it’s a very identifiable sweatshirt. It’s clearly the one that’s on the scene that he was wearing during the shooting.”

The Samaritan ultimately helped investigators identify Sykes by selecting an image of him out of a photo array, law enforcement sources said.

The principal of Campus Magnet High School also identified Sykes after cops showed him still images of the suspected shooter, and provided a school photograph of the sought teen, the sources said.

The NYPD has “probable cause” to arrest Sykes, and investigators with the Regional Fugitive Task Force were “contacted by an attorney, hopefully, possibly to arrange his surrender,” the chief said.

“What we’re getting from our victim’s friends is that Flex is a known troublemaker in the area,” Kenny said. “And we have on video from the Dunkin Donuts – a male as the interaction is going on, where they’re taunting each other, he’s saying, ‘Flex is gonna die. Flex is gonna die.’”

Sykes has several social media postings showing a blood drop, “but he does not specifically mention any gang in his social media,“ Kenny said.

He was previously arrested on Oct. 12, 2023 for robbery and on Dec. 8, 2022 for gang assault, sources said.

The teen was processed as a juvenile delinquent and those cases have since been sealed, according to the sources.

The NYPD on Thursday released two photos of the suspected shooter — one of him holding a gun in his hand while running, the other a close-up of his side profile.

He was described as a male with dark complexion last seen wearing a black hoodie, black pants, white sneakers and a backpack with the “JAWS” logo.

As the NYPD was hunting for the suspect, Samuel’s family was only keeping the teen’s body hooked up to a ventilator in hopes of donating his organs, Kenny said.

Anyone with further information on the case is urged to call the NYPD’s Crime Stoppers Hotline at 1-800-577-TIPS (8477), or for Spanish, 1-888-57-PISTA (74782).

The public may also submit tips online at Crime Stoppers website or via X @NYPDTips.