I want to know if I give up my paternal rights as a father will I be terminated from all responsibilities including child support

Please pay more attention to sticky notes posted on the top of each forum. Generally they contain answers to frequently asked questions like yours. Had you not ignored them you might have read this:

https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html

Which answers your question

By the way its PARENTAL rights and no you can't just give them up.

If the other parent has a step parent that wants to adopt, you may sign over your rights and no future child support is due, ( often back support would still be owed)

But you can't just give up your rights, for other reasons, and if for some reason they could would let you, no it does no stop child support