Berkery has ben living rough and busking on the streets and living in a shelter in New Jersey.
And now he wants his famous father to let him come and see him 'before it's too late.'
The 78-year-old music icon was forced to cancel two shows after he was hospitalized with a bacterial infection.
He revealed: "He's not well, I think he's pushing himself too much.
'I reached out to his son Mark, my half brother, last year to see if I could arrange a meeting.
"Now I refuse to wait – I want to see my dad and make my peace with him."
Sir Tom took to social media to reassure his fans about his condition.
He told them he was 'sorry and disappointed' about missing shows but that he hopes for a 'speedy recovery.'
Jonathan was born after the Welsh superstar enjoyed a three-day fling with Katherine Berkery, then a 24-year-old model, in New York in October 1987.
Sir Tom denied he was Jon's father until it was proved by a court-ordered paternity test in 1989.
The 'It's Not Unusual' singer agreed to pay $2,700 a month maintenance for his upkeep until his 18th birthday but was not involved in his life.
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