What rights do prisoners have regarding their children?

my granddaughters father is now in prision, does he have rights to the child if my daughter wants to give her baby up for adoption

That would depend on the crime he committed, the length of his sentence, and state laws and restrictions. He and you should look into all of these to ascertain the rights of parenthood that apply to your granddaughter's father. This is a case that must be handle through legal means. You could cause great emotional damage to the girl, her father, an adoptive family if you do not get this right.

He does to a point. The adoption agency always asks for the consent of BOTH parents. He may be able to dispute the adoption BUT it also depends upon the seriousness of his crime. If he's in prison and is serving a life sentence, no one is going to give him a child. The child's father's parents also have rights to the child.

The short answer is - He is the parent until his parental rights are terminated.

The long answer is complicated. If he's in jail for a crime against the child, his rights are limited, but until they are terminated, he is the parent. Period.

If he's in jail for a different crime, then he is the father. He has a right to be appraised of all developments, a right to be present at hearings (yes, they have to transport him), a right to have a say in anything that happens to his child.

thad depends if the prision wants the children want to be adopted or not

He shouldn't have ANY! He's in JAIL! He should have all rights & privileges taken away from him. That's SUPPOSED to be the purpose of prison.