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When applying for naturalization, can I include my child born outside US in the application?
No
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If not, after I get naturalized as a US citizen, can I sponsor green card/citizenship for my child born outside US?
Yes, you can petition for your child to get a green card. But you can already do that right now as a permanent resident if the child is not married (the wait times are slightly different; you can always upgrade the petition once you naturalize).
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How long will it take for the child to get green card/citizenship?
It depends on the category and their country of birth. See the latest visa bulletin. Children under 18 of a U.S. Citizen is always no wait. Unmarried children over 18 of a citizen (F1) currently has about a 7 year wait for most countries. Married children (F3) currently has about a 10 year wait for most countries.
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In the meanwhile, can I bring my child to U.S on a Visa?
The child can apply for a U.S. visa. There is no guarantee they will get it, or if they get it, that they will be let in.
