
Quoting
USCIS
A child who is ... born to one U.S. citizen parent and one alien parent or two alien parents who naturalize after the child’s birth ... can become a U.S. citizen by action of law on the date on which all of the following requirements have been met:
o The child was lawfully admitted for permanent residence*; and
o Either parent was a United States citizen by birth or naturalization**; and
o The child was still under 18 years of age; and
o The child was not married; and
o The child was the parent’s legitimate child or was legitimated by the parent before the child’s 16th birthday (Stepchildren or children born out of wedlock who were not legitimated before their 16th birthday do not derive United States citizenship through their parents.); and
o If adopted, the child met the requirements of section 101(b)(1)(E) or (F) and has had a full and final adoption; and
o The child was residing in the United States in the legal custody of the U.S. citizen parent (this includes joint custody); and
o The child was residing in the United States in the physical custody of the U.S. citizen parent.
If you and your child meet all of these requirements, you may obtain a U.S. passport for the child as evidence of citizenship. If the child needs further evidence of citizenship, you may submit an "Application for Certificate of Citizenship" (Form N-600) to USCIS to obtain a Certificate of Citizenship. If the child meets the requirements of Section 101(b)(1) of the Immigration and Nationality Act as an adopted child, you may submit an “Application for Certificate of Citizenship on Behalf of an Adopted Child” (Form N-643). (Note: a child who meets these requirements before his or her 18th birthday may obtain a passport or Certificate of Citizenship at any time, even after he or she turns 18.)
*NOTE – Children who immigrate in the “IR-3” or “IR-4” categories must have had an immigrant petition filed on their behalf before their 16th birthday; see answers to Question 25 below. All adoptions for any other type of immigration benefit, including naturalization, must be completed by the child's 16th birthday, with one exception: A child adopted while under the age of 18 years by the same parents who adopted a natural sibling who met the usual requirements.
**NOTE – The “one U.S. citizen parent” rule only applies to children who were under age 18 on or after February 27, 2001. For children claiming automatic citizenship prior to this date, the individual in certain cases would have to establish that the parent or parents who were not U.S. citizens by birth had naturalized (or that the naturalizing parent was separated or legally divorced and had legal custody of the child).