I've read different accounts though on the laws regarding conferring citizenship to an underage mother's child, whether the birth occurred in or out of the country.
It is a well established fact the father was not a citizen, therefore zer0 is not eligible. But that would only count in a country where race doesn't trump the law.
Father did not have to be a U.S Citizen if he had a “Green Card” or was a perment resident. He was here on a student Visa.