You have to submit your Naturalization Cetificates, your marriage certificate, her birth certificate, her green card, etc.
Mr. Shusterman's (former INS Trial Attorney, 1976-82) response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
Become a citizen first. Then, check your child is still under 18. Then read the instructions to N600 and follow them. On your facts, the child under 18 will become a citizen by operation of law on the day of your Naturalization. N600 is a technicality you will be doing to memorialize this fact the child and make the child's life easier in the future, not to make the child a citizen.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.
As you state; you are a citizen through Naturalization via refugee status.
Me colleague has provided you with a list of doc's needed.
You child is a citizen. The N-600 is a means for getting him a Naturalization Certificate. once he gets his certificate you need to get him a USA Passport.
Kyndra L Mulder, Esquire
Office at 4110 Southpoint Boulevard (Across the street from the USCIS)