If the father of my child gives up his rights will I lose my child care assistance?

This should really be posted under "Family Law" so I've requested that your thread be moved.

There is a sticky at the top of the Family Law forum regarding termination of parental rights which you can read here:
https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html
It's not a easy process and the courts are hesitant to do it unless there is another party willing to adopt the child. Also, if you're receiving state assistance I'm sure the odds of them "letting him off the hook" so to speak would be slim to none - the state will want him to be held financially responsible for his child which he helped create, not simply place the burden on the taxpayers.

Please pay more attention to the instructions on the screen. The title box is only to briefly describe your question. For us to help you, you need to provide details. That's what the larger box is for.

I'm not sure where you get the idea that the father can give up his rights. By child care assistance, do you mean his child support or public assistance.