It happened just after midnight on Sunday at Central Avenue and 92nd Street.
Family members say 30-year-old James Vargas was with his wife and kids when they stopped to get food at a nearby taco stand.
As he was getting out of his car, the father was shot and killed by a man accusing him of being a part of a gang. James Vargas' son reportedly witnessed the shooting.
"When [Vargas] was getting out of the car, some guy in a Tahoe pulled up on him and asked him where he's from and what gang he was affiliated in, and he didn't give my brother a chance to say anything ... just shot him right there," said Kathy Vargas, James Vargas' sister.
The victim's family says he was not a gang member and says he has never been affiliated with any gangs.
"My brother is not part of any gang," said Billy Vargas. "He's a family man raised in a good family, good upbringing ... He was a hard-working man, providing for his family."
James Vargas' siblings say the father's main priority was always his family.
"Still feels like a dream," said Manny Rivero, James Vargas' brother-in-law. "Can't believe he's gone. I can't process and accept that James is not here, physically, on Earth."
Meanwhile, witnesses say the gunman and the gunman's driver took off in a green Chevy Tahoe.
The family pleading for the public's help in tracking down the suspects. A GoFundMe has been set up to help James' Vargas wife and children.