Authorities grilled the boyfriend of a New Jersey mom whose 5-year-old daughter was apparently abducted in connection with her disappearance — after learning he’s an illegal Mexican immigrant, according to a report.

Noema Alavez, 19, said her boyfriend, whom she did not identify, was questioned this week about the suspected kidnapping of Dulce Maria Alavez from Bridgeton’s City Park on Monday.

Alavez, who is five months pregnant, said she believed the boyfriend was now being held in federal custody and may be deported, but federal officials could not confirm that Wednesday, the Inquirer reports.

A federal source confirmed to The Post early Thursday that Alavez’s boyfriend, Edgar Martinez, 27, was in Immigration and Customs Enforcement custody.

The girl’s father, meanwhile, has returned to Mexico to study at a university in Sinaloa after staying with Alavez, a Bridgeton native, for a short time, the newspaper reports.

“He’s finishing his studies so he could give a better life to my daughter,” Alavez said.

The distraught mother said she had not eaten for 36 hours at one point during Dulce’s disappearance and that people — including a search volunteer — had told her she wasn’t “going crazy enough,” she told the Philadelphia Inquirer.

“’If my daughter was missing, I wouldn’t eat!’ this lady yelled at me,” Alavez said. “Then she started taking a video of me. My mother told me not to go back to the park because everyone is talking bad about me.”

Detectives have also been skeptical of Alavez, she said.

“The police tell me, ‘If you know where she is, tell us,’” she recalled. “But I told them everything. They think I’m lying; I’m telling the truth.”

An Amber Alert remained in effect early Thursday for Dulce, who police believe was abducted from the 1,000-acre Bridgeton City Park, where parents and families said Wednesday that they still feel safe despite the suspected kidnapping, NJ.com reports.

Residents told the website they felt secure with the additional police presence there and had no reservations about going to the public space just days after Dulce was apparently abducted by a light-skinned white or Hispanic man who drove off with her in a red van on Monday.

“If anything I’ve felt safer than before because the cops are all around,” one woman who took her great-granddaughter to a zoo inside the park told the website. “I decided that I was going to drive past and if there were no cars and no other people here, we wouldn’t stop. But I saw the cars so we came in.”

Another woman who was also at Cohanzick Zoo said she didn’t think twice about taking her son there on a Wednesday afternoon, while a pair of sisters inside the park said they were praying for Dulce to be found unharmed.

There were few signs of an active ongoing search by law enforcement at the park Wednesday aside from helicopters scouring for clues from above. On Tuesday, the hunt for Dulce involved K-9s and a dive team, as well as a helicopter, NJ.com reports.

Bridgeton Police Chief Michael Gaimari said Wednesday that investigators have obtained as much video surveillance from the area as possible, but are still no closer to finding the girl, who vanished as roughly two dozen people were playing basketball at a nearby playground.

“We don’t have any solid suspects,” Gaimari told WPVI. “We are investigating all the possibilities.”

Dulce’s 3-year-old brother, Manuel, who was playing with her at the time, has said she disappeared as they played near several storage buildings next to the playground.