See the following at:
Naturalized U.S. Citizens: Proving Your Child’s Citizenship | LawHelp Minnesota (lawhelpmn.org)
When a parent becomes a citizen, are the children automatically citizens?
The child may be a U.S. citizen if ALL these things are, or were, true at the same time:
- The child is under 18 years old.
- The child is a legal permanent resident of the U.S. (has a green card)
- At least one of the parents is a U.S. citizen by birth or naturalization. If that parent is the father but not married to the other parent, talk to an immigration lawyer.
- The citizen parent is the biological parent of the child or has legally adopted the child. A step-parent relationship is not enough for derived citizenship. Talk to a lawyer if the citizenship is for an adopted child because there are special rules about this.
- The citizen parent has shared or sole legal and physical custody of the child.
If these things are all true, your child automatically becomes a U.S. citizen in most cases. But you need to get proof of citizenship for the child. You can do this by getting a certificate of citizenship or a passport book or passport card.