What is my chances of getting a green card through my child?

If your child was born in the US then you have a better chance especially if you the child's mother it depends on how you came into the US

This was answered here by experts: https://www.askmehelpdesk.com/immigr...en-391211.html

Depends on a lot of factors you haven't taken the time to tell us about your case...

It took me several YEARS to get my wife a green card... and I was always a US Citizen, and she was never here illegally to complicate things.

Just so you know its neither simple, cheap... easy or automatic.