I live in Arkansas and I have power of attorney for my father he is 62 years of age and on disability has had several small strokes and can barely walk and speech is about gone he is on a fixed income but a lady is stating he is the father of her 2 year old son, she is now requesting childsupport from him the paternity test shows this is his baby my question is if he gives up his rights to this child is he still responsible for paying childsupport and will we have to hire an attorney for this process or can we just tell the judge when he goes for his childsupport hearing?

He can terminate his rights, but he is still going to be financially obligated to this child, unless they find him falling below what is called a "minimum needs standard" which means if he paid child support, he would not have enough money to live. Perhaps you should try to settle this out of court with the mother, explain the situation and see what happens. However if she wants to still pursue this in court, you NEED to get a lawyer, it is in your best interest. (I highly recommend a MALE attorney for your side of the case)

Sounds like you have a young brother, so of course you should want your father to do the moral and legal responsilibty for his actions.
** but then it sounds like you don't

But giving up rights has nothing to do with his payment obligations to pay support, and while you can use an attorney, he can not get out of paying his support payments.