A Your question does not state when you became a U.S. citizen, or if you are a natural-born citizen. For the purposes of answering this question, I will assume that you are a naturalized citizen.
In February 2001, a new law went into effect which provides that children who are under 18 may automatically derive citizenship when one parent naturalizes, as long as the children are Legal Permanent Residents and are in the legal and physical custody of the naturalizing parent. If you naturalized before the new law, your child under 18 became a U.S. citizen on the date the law took effect: February 27, 2001.
According to the regulations, your child does not have to be legally present in the United States at the time of your naturalization, but he/she must begin to reside in the country as a lawful permanent resident while under the age of 18 in order to derive citizenship from you.
Additionally, your child under 18 may automatically derive citizenship upon your wife’s naturalization provided that he/she has been listed on your wife’s Form N-400 and that one of the following conditions is met:
• The child’s other parent is already a US citizen; or
• The child’s other parent is naturalizing at the same time; or
• The child’s other parent is deceased; or
• The naturalizing parent and the child’s other parent are legally separated and the naturalizing parent has custody, or
• In some cases, if the naturalizing parent is the mother and the child was born out of wedlock.
If your child automatically derived citizenship when you naturalized you do not need to file any special papers with United States Customs and Immigration Services (USCIS). However, it is a good idea to obtain some proof of your child’s citizenship. You can do this by submitting Form N-600, application for certificate of citizenship to the USCIS.
Q Under what circumstances is an I-485/AOS interview scheduled?
A Certain types of applications always have interviews. These include cases with any criminal history, even if the matter does not prevent the approval of the I-485 AOS (Adjustment of Status) application. Cases with past immigration violations of a serious or extended nature are also often selected for interviews.
Interviews may also occur in cases involving labor certification substitutions (due to concerns about fraud). Questions about the job offer may be prompted in “future employment” situations when the beneficiary has not worked for the employer sponsoring the permanent residence, etc.