thank you!

Is a child a citizen of the USA under section 320 of INA (child citizenship act)?

A legal permanent resident (LPR) child lives with LPR natural mother and us citizen step-father. Step-father, LPR natural mother and LPR child moved outside the United States on official US government military orders. While outside the United States, and before LPR child reached 18 years old, LPR natural mother became a US citizen. Did LPR child automatically derived US citizenship under section 320 (from mother), despite living outside the United States on official United States government/military orders? The child returns to the USA after he is 18 years old.

Is the child considered "residing in the United States" for the purpose of the Child Citizenship Act by being a dependent (step-son of a US military personnel) on US government orders overseas residing with natural mother? The state department below appears silent on the definition of "residing in the United States". Has anybody had this trouble too and received a passport or Certificate of Citizenship?

A child who has lawful permanent resident (LPR) status will have a permanent resident card (green card). Another way to show LPR status is the I-551 stamp in the child's passport. This stamp shows that the child has entered the United States on an immigrant visa and/or has been admitted as a lawful permanent resident. Admission as a lawful permanent resident alone does not establish that the child is residing or has resided in the United States; that requirement must be established separately. (See below for additional information.)

How to Show That a Child Is Residing or Has Resided in the United States:

Mere entry into the United States or a temporary visit - even if on an immigrant visa - does not meet INA Section 320’s requirement that the child be "residing in the United States." Determining whether a child is residing/has resided in the United States typically rests on an analysis of both the character and the duration of the stay. A parent may be required to provide supporting evidence regarding a child’s stay in the United States in the legal and physical custody of the U.S. citizen parent(s) in support of the child’s passport application.