This depends on many factors. Generally, a United States citizen parent may file a a petition for their adopted child to become a lawful permanent resident if the child was adopted while they were under 16 and they have resided in the legal custody of the adopted parent for 2 years. The child must be under 21 when the petition is filed. Depending on how the child entered the United States (with or without inspection) they will either receive residence in the US or have to go overseas to receive their visa. The government will likely want to know why the child was not placed on the other immigration forms, however, you can offer an explanation for this. If the adopted child becomes a resident before they turn 18 through sponsorship by the US citizen parent, they will automatically become a US citizen as well. This is a complicated area of law and I highly recommend that you seek the advice of an immigration attorney.
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