Grandson here almost a month seen mom 3 times because it was something she needed for her. The state helps her, and she spends money on her not son. Would like to get custody.

Is there a father in the picture (or is he known, if not)?
How is the mother related to you (you make it sound like she isn't your daughter)?
It won't be easy to get custody if the mother doesn't want to give up her benefits. And fighting her might mean that she will take the child away and you won't see him at all. So be careful. It would be best if you work out a mutual agreement. If you can't, go to Family Court. I'd talk to a social worker first. 3 times in almost a month isn't that bad as things go when a mother drops a child with a parent.