I've been lived with my EX for 4 yrs. We have a 6-year-old son. We had broken 3 years ago. But we are still living together, because we bought a house together. And we are taking care of my child together also . Now I want he give me a full child custody, he denied it. And his mother, my child grandma is going to take my son to somewhere this summer. Can I need to file child custody? And can I apply the child support even we are living together? For the past 3 years he didn't get me any money.

Since you live together, a court would view that as having joint physical custody so there would be no support ordered, most likely.