Children below age 18 cannot file Form N-400 for naturalization and they need to turn 18 in order to apply for U.S. citizenship. If you the parent or your spouse is a U.S. citizen, your child will automatically become a U.S. citizen.
If your child was born outside the U.S. and you or your spouse were a U.S. citizen at the time then you just need to file a petition for a citizenship certificate (Form N-600) for your child. If approved your child will receive a certificate of citizenship which would help prove their citizenship status.
Similarly, if you are a naturalized U.S. citizen and if your child was a minor below age 18 when you received your naturalization certificate, your child can acquire citizenship from you and obtain a citizenship certificate, by filing Form N-600, Application for Certificate of Citizenship.
If you are a Green Card holder and are applying for U.S. citizenship, your child can also become a U.S. citizen at the time you obtain your U.S. citizenship, provided you entered the name of your child under age 18 in the citizenship application Form N-400. Your child below age 18 will become a U.S. citizen when you become a naturalized U.S. citizen.
And you can apply for U.S. passports for yourself and your child and remain as U.S. citizens, anywhere in the country. However, if your child is not a minor below age 18 when you become a naturalized citizen then a separate application for naturalization must be filed for your child. Remember your child must be a green card holder and above age 18 to file an application for naturalization.
Your child can obtain a citizenship certificate even if you were not a U.S. citizen and if your spouse was a U.S. citizen and vice versa. In this case, your child’s birth certificate must contain the name(s) of his/her parent(s) who were U.S. citizens, when they were born.
Likewise, if you or your spouse or both became naturalized U.S. citizens before your child turned 18, he will automatically become a U.S. citizen. As the naturalization laws differ, you will have to be aware of the citizenship laws that were in effect at the time of your child’s birth.
Your child cannot automatically become a U.S. citizen, when you become a U.S. citizen, if he/she is not a permanent resident and if he/she is an undocumented immigrant.
Your child can acquire citizenship from you only after he/she becomes a lawful permanent resident. If your child does not meet the N-600 requirements, he/she can apply for U.S. citizenship only after turning 18, by filing Form N-400.
If your immigration case is unique and you need more information it is recommended to consult an immigration lawyer.