Would I have to pay expenses in child support if the mother of my child is on public assistance

Usually yes. If a mother applies for public assistance, they are required to name the father and the support agency will require that a child support order be sought.

So I will basically be paying for things that are free which doesn't make sense because my daughter and the mother of my child is on medicare

Maybe I misunderstood your question. But othing is free. If there are services being paid by public tax dollars because the custodial parent can't afford to pay for them, but the NCP is not paying their fair share, then they will be required to pay their fair share.

Are you currently under a support order and paying the ordered amount?

You are paying the state back for money it pays her that it may not have to, if you were not a dead beat and would be paying support like you should

No I'm not on child support yet

Then be ready to be ordered to pay retroactive child support!

Well maybe if you had paid child support they wouldn't have had to go on public assitance.

They will go after you for payment, so basically what they're doing is giving HER money and then going after you for support to pay it back to THEM. If you are ordered an amount more than her grant amount, she will receive the difference. If you are ordered an amount less than her public assitance grant, it will all go to them.

It makes sense because it's your child. Public assistance doesn't appear out of thin air. It comes from the taxes of people who go to work everyday. Taxpayers shouldn't have to pay to raise your kid.

so i will basically be paying for things that are free which doesnt make sense because my daughter and the mother of my child is on medicare

It's not free! I pay for it out of my taxes. Where do you think the money comes from?

... Where do you think the money comes from?
Government printing presses, essentially.

Government printing presses, essentially.

Yeah, so that would get us out of the national debt then right?