[GringoCArlos]

The father needs to go to the US Consulate in Santo Domingo to apply for a Birth Certificate for US Citizen born Overseas. (at this moment, the baby is a dominican without a valid US travel visa) He will most likely have to run around getting documents for a day or two.

The father will need his birth certificate, passport, and whatever other documents are required (this information should be on the US State Department or the Santo Domingo Consulate websites). A Dominican birth certificate naming him as the father isn't sufficient evidence (too much previous visa fraud by many others).

Because they are not married, he and the baby will need to get a DNA test done by a lab which has been approved by the US Consulate, to prove the blood relationship and his fatherhood. Then he will need to present the test results and his identification papers back to the US Consulate. IF they approve, they will issue the US Birth Certificate.

If the mother does not have a US visa, then the father and she will then need to obtain permission to have his baby (with the new US Citizenship) accompany him to the US without the mother. This involves more running around getting documents and permissions stamped before he will be able to legally exit the DR with his minor child to go to the US for treatment (even on a medi-vac flight). The mother and father must appear in person to get these documents, or else have notarized documents if one is absent)

Finally, the last question - does daddy have medical insurance in the US for his sick child - if not, maybe the Shriners or another organization can help them.