As has been said above, this is a UK-based site, where very few people will be familiar with US laws and legal procedures (which are vastly different to those of the UK). So I'll suggest that you try this US-based website instead:
https://answers.yahoo.com/
However, as I read your question, it relates mainly to the correct wording of a letter (rather than to detailed legal procedures), so I'll attempt a rough draft for you anyway:
"To [name of relevant court or judicial body]
Sirs,
On [relevant date], [name of court] ruled that I am the father of [full name of child] and made an order against me for the payment of maintenance to [full name of child's mother] in respect of support for the aforementioned child.
The said order was made without DNA evidence being available to the court. This was because I was a prisoner at [name of prison] at the time and thus unable to provide the Court with a DNA sample (which , I am confident, would have shown that I am not the father of the said child).
I am now both willing and able to take a DNA test and I earnestly request that, in interests of natural justice, the Court case be re-opened in order that I may show that I am not the father of [full name of child] and that the order made against be should therefore be quashed"