Can a single mom apply for green card if her 8 yrs old child is US citizen?

Yes, a single mom can apply for a green card if her 8-year-old child is a U.S. citizen. The child can sponsor her for a green card once they turn 21, but in the meantime, the mother may explore other options, such as family-based Immigration through a different qualifying relative or applying for asylum if applicable. It's advisable for her to consult with an immigration attorney to understand the best pathway based on her specific situation.