Can I file the affidavit of paternity as my baby was born overseas and I (father) am in the US as a visitor?

However, if you're a visitor here, do you normally live in the same country as the child. The country in which the child lives has jurisdiction. So where she was born is not relevant. Where the child is now is what's relevant. If she isn't where you are, any action needs to be filed where she is not where you are.