Medicaid insurance question

So I talked to my case worker today. They went ahead and added my son who was born in June to get health and food assistance. For one, I never asked for the food assistance. For 2, they made an error on his health insurance and it was only good for 2 weeks. Anyways when we was talking she started asking me about my sons dad. Asked his name, birthdate so I told them then asked if I knew his social security number. That’s when I was like I’m not sure, although he was with me I asked why. She says for child support. Well, I’m actually with his dad like we’re in a relationship. She said that basically his dad will be responsible for food as well. I told her I would call her back and let her know because I don’t think it’s right he pays child support for food benefits while we’re together. He’s not a dead beat dad and would do anything to help his son so I’m not worried about it. Well I called her back a few times she didn’t answer then she answered and yelled at me told me I can’t call like that and was pretty rude then hung up on me. All I was trying to do was reach her and ask some questions before she submits my stuff to friend of the court. Anyways, no. I don’t want my sons father on child support so we agreed for my son to not get food benefits to just skip that part of the process. However since she wasn’t able to answer my question I’m currently wondering if that affects his health insurance or will he be able to qualify for state health insurance regardless? I’m asking here because someone might know or may have gone thru something similar. If we need to go to court to sort out paternity that’s fine but I don’t want him on child support but for my son to get health insurance because my baby daddy doesn’t get health insurance benefits thru his job…