Your foreign-born ancestor who immigrated to America as a child and who was under the age of majority when his father naturalized would have become a citizen based on that father’s naturalization.
Children of the father who were over the age of majority would not have become citizens via their father’s naturalization.
Before the early 20th century in the United States, the citizenship status of a woman was tied to that of her husband throwing an additional complication into the mix.
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