Overstayed a Visa, Left the U.S., then Married a U.S. Citizen

[non sequitur]

The alien returned home after overstaying her Visa by 15 months. She subsequently gave birth to the child of a US citizen and married the US citizen in her home country (in that order).

What are the alien's chances of being able to enter the US?

Is the child a US citizen by virtue of being fathered by a US citizen who acknowledges paternity and has now married the mother?

Thank you.

[Mr. Knowitall]

She's subject to a lengthy period of exclusion due to the overstay. Her spouse was able to marry and apparently live with her overseas and her child is not in the U.S., so there's no sign of hardship from the exclusion. So her odds seem low until her bar against reentry expires.

The father should take appropriate steps to register the child's birth with the U.S. Embassy or Consulate in the nation at issue.