How can i cancel a child support case that just begun, with a court date coming up, when me and the dad live together with our child?

You should both go to the child support office and let them know you live together. However, if the child is on Medicaid, the case was probably initiated by the Texas Attorney General. That issue will need to be addressed in some way. The state is trying to get reimbursed from the father for the medical assistance it's providing to your child.