HI, what is the process for the legally incapable daughter of USA citizen to get citizenship?

Question

the daughter is 31 years old and lives outside USA.

Answer 1

Could you please provide some more information. How is the daughter incapable? How did the U.S. Citizen become a citizen? Is the 31 year old married?

It doesn't sound like she would be eligible for auto citizenship. The mom would have to apply for an immigrant visa for her. If she put her daughter as a dependant on her original visa application it will be easier. Where outside the US is she living? Can she live by herself?