How or can I even get any kind of custody of a child who is not related to me, but I have been caring for him when he was born to this day? And his mother do not wish to get over right or anything else she nor the father has done any thing. And she decides one day she just want him. What should I do? Can I get back child support from them?

No you can't get back child support for the child because none was ordered to be paid. When you had possession of the child and they lived with you was the time to address it. You can get guardianship of the child. And after your awarded that then ask for child support. And then create a track record to later adopt the child.