The Long Island mother of Kansas City Chiefs football player Jovan Belcher told investigators her son argued with his girlfriend Kasandra Perkins over their baby’s paternity before he shot her dead and killed himself, The Post has learned. Cheryl Shepherd — who was in her son’s suburban Missouri home the morning he shot Perkins nine times — told investigators after the shootings that there were questions about whether the West Babylon, LI-raised linebacker was the father of the couple’s 3-month-old daughter, Zoey, said sources familiar with the situation.

“The mother believed that there was an issue over whether [Belcher] was the father,” said a source close to the Chiefs with knowledge of the situation.

“She said he [believed he] wasn’t necessarily the father of the child.”

A Kansas City law-enforcement source confirmed, “She told [police] there was a question about the paternity.”

It’s unclear if the paternity issue was the reason for the final, violent end of the troubled relationship between Belcher, 25, and Perkins, 22.

“But the implication was that [paternity] was what the two of them were fighting about — that the baby might not have been his,” a source said.

Belcher fatally shot Perkins at 7:50 a.m. Dec. 1 after a heated argument that started at 7 a.m.

Shepherd, who had been visiting the couple, called 911 after her son fled the bloody scene.

Before bolting, Belcher apologized and kissed the dying Perkins and their baby daughter good-bye, according to the Kansas City Star.

He then drove to his team’s practice facility and shot himself in the head in front of the team’s coach and the general manager.

Asked by a reporter this week to elaborate on details of the fight and the paternity comments made to police, a woman who answered Shepherd’s cellphone said, “There will be no comment.”

The woman, who declined to identify herself, said Shepherd “doesn’t have anything to say about that.”

The Chiefs had been providing Belcher and Perkins with counseling for relationship and financial issues, police have said.

Under the surviving-child benefit of the NFL’s collective-bargaining agreement, little Zoey stands to receive more than $1 million.

NFL players-union spokesman George Atallah did not respond to several calls or e-mails asking whether the payout plan was contingent on a paternity test.

The child is slated to get $108,000 annually over the next four years, $48,000 in the fifth year and then $52,000 each year until she’s 18 — or 23, if she attends college.

Belcher’s beneficiary also will get $600,000 in life insurance, a $100,000 retirement account and $200,000 for each season he played. Belcher was in his fourth season with the Chiefs.

A Kansas City police spokeswoman said the baby’s paternity wouldn’t be part of the department’s murder-suicide probe.

“That would not be something they’re going to investigate,” said Sgt. Marisa Barnes. “It’s a ‘he-said, she-said’ so there’s no way to investigate. It would be nothing more than a civil matter.“

Police are expected to wrap up their investigation and present it to prosecutors as early as this week, Barnes said.

The night before the fatal argument, Perkins had been to a concert with friends. Belcher went out for dinner and drinks with another girlfriend, and cops found him passed out in his Bentley outside her apartment complex at 3 a.m. Belcher went back into the building to spend the night after cops woke him up.

Belcher and Perkins started dating in 2010 after being introduced by her cousin, Whitney Charles, who is married to Chiefs running back Jamaal Charles.

Zoey was born in September, and Facebook photos show a beaming Perkins and Belcher showing off their bundle of joy.

But the couple’s relationship was rocky. Perkins returned to her native Texas around Halloween, and later briefly moved in with Whitney and Jamaal Charles, friends said.

By Thanksgiving, Perkins was back with Belcher in their modest, three-bedroom home.

Belcher’s mom has temporary custody of the baby, but a permanent guardian has not been named.

Perkins’ family — who brought Zoey to a Texas memorial for her slain young mom last week — indicated that they will be involved in her upbringing.

“We will raise Baby Zoey in the knowledge of the love from which she was born,” Perkins’ family said in a statement.

The “loyal, honest and trusting” Perkins, they said, “was dedicated to starting her new family and beyond excited about being a mother to her sweet baby.”

There was no mention of Belcher at the service.

Family members declined to comment on the paternity issue.

“There has been a disheartening amount of rumors and speculation surrounding the tragic loss of our Kasi,” the family statement said.

“No one will every truly know why this happened, nor is there anything to be said that could justify or ease our pain.”

Additional reporting by Amber Sutherland in Austin, Texas, and Tara Palmeri in Kansas City, Mo.