Is it possible for a US born dual UK citizen to sponsor their child?

Ok I’m 26 definitely not a child, but mom was born in the US and holds dual citizenship with the UK. She’s lived in England for about 5-6 years now. I’m wondering if she could eventually sponsor me.

I’m starting a postgraduate course this fall, but will have a student visa for the duration of the course. I also understand there a 2 year visa for individuals who recently graduated. I would like to live close to her once I graduated, rather than going back to the US. We’re super close and I’m an only child—our family is very small.

I looked for a while online and couldn’t find information relating exactly to my question since I’m over 21.