A child born abroad out-of-wedlock to a U.S. citizen father may acquire U.S. citizenship under Section 301(g) INA, as made applicable by Section 309(a) INA provided:
1) a blood relationship between the applicant and the father is established by clear and convincing evidence;
2) the father had the nationality of the United States at the time of the applicant's birth;
3) the father (unless deceased) had agreed in writing to provide financial support for the person until the applicant reaches the age of 18 years, and
4) while the person is under the age of 18 years --
A) applicant is legitimated under the law of their residence or domicile,
B) father acknowledges paternity of the person in writing under oath, or
C) the paternity of the applicant is established by adjudication court.