N-600 is intended for your children to obtain a certificate of citizenship as proof of their citizenship. Please read that carefully, "proof of citizenship". It is not to obtain citizenship because they do that automatically when you naturalize (as long as they meet the requirements of the child citizenship act of 2000, basically under 18 years of age, in your legal and physical custody and having a green card). For proof of citizenship you have the option of applying for passport (book and/or card) and/or applying for N-600 (certificate of citizenship). Passports are cheaper and faster to obtain. Certificates are more expensive but don't expire and create a record of citizenship within USCIS. I mentioned that you can apply for N-600 at the same time you apply for your passport because you only need to send photocopies of documents with the N-600 application, so you don't need to wait for your original certificate to come back after applying for your passport. The other point is that you cannot send N-600 application before you naturalize, as your son doesn't become a citizen until you complete your oath. I hope I haven't made it even more confusing.