Question: Does anyone know if there is a time limit (years) to where a father can claim a child to be his then recant? 

Answer: Once he signed the LEGAL birth certificate, he became the legal father of that child. A birth cert. is a legal document. If he wants to pay for a paternity test, let him flip out the bucks, it's just going to be a waste. In the meantime, I would be back in the court asking for extra money considering your sons illness. God bless you!
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