I take it that your kids were NOT born in the US (otherwise they are already US citizens). If they are under 18 years of age AND legal permanent residents AND residing with you then you do not need to apply separately for them. They will automatically become US citizens when you take your oath. They will not get a certificate of naturalization automatically but you can obtain one by filing N-600 on their behalf after you have naturalized. But the better alternative is to apply for their passports (this can be done based on your certificate of naturalization) and use that as their proof of citizenship. If your kids are over 18 years of age they need to apply separately. If they are not yet LPRs then they will derive citizenship from you only after becoming LPRs.
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