The county I live in closed my child support case for the reason of the father being permanent diabled. Am I stll able to get some type of support or apply for benefits for my child since his father gets social security?

Certain types of social security disabilities do allow for payments to the disabled's children. You should go with the father to the SS office to apply.

What type of social security is he on? If it is SSI then there is no benefit for the child. If it is SSD then there may be a benefit for the child.