The singer's former girlfriend Caterina Lopez claimed on social media that he "doesn't deserve to call himself a parent".
In posts on Instagram and Twitter earlier this year, the American actress, 29, described herself as a "single mother" to the little boy – who underwent his fourth operation to treat a rare brain condition in New York in August.
Caterina – who split with 30-year-old JJ in April 2016, before getting back together briefly last year – wrote in June: "This year I will be advocating for stricter laws against parents who abandon their children especially parents who abandon their children that are chronically ill or have a disability.
In another from July, she shared: "Always fight for your child especially when no one else is fighting for them.
A video clip from Instagram from October, showed her friend Eva Longoria visiting Princeton in hospital.
In a post from November, Caterina shared a video of her and with her son out of hospital and riding in a helicopter.
The Sun Online has contacted a representative for JJ for comment.
In April 2016, The Sun revealed that the Union J band member had had a secret fling with Casey Batchelor, 33, while on a break from Caterina.
JJ told The Sun Online that the Celebrity Big Brother star "meant nothing" to him.
He said: "It was just a short thing and it meant nothing.”
The star added: “Caterina was a little bit shocked but she’s fine now. We’re happily, madly in love. Things happen. She’s very understanding.”
A friend of Casey’s told The Sun the previous month: “Casey was raving about him and thought he was a great guy.
“She has been treated badly in the past and is a sucker for love, so it was shocking for her to all of a sudden see that he and Caterina had reunited.
“He didn’t tell her they were getting back together.”
Of his relationship with Caterina at the time, he gushed: " “She’s hopefully, eventually going to be my future wife.”
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