Fathers of unborn children have few legal rights when it comes to their child. While some states grant fathers of unborn children specific legal rights in a limited number of circumstances, most rights over the child fall to the mother. Your rights as the father of an unborn child are dependent upon the state in which you live, and you should always talk to a qualified attorney in your area for up-to-date developments in this area of the law.
The primary right fathers have to their unborn children pertains to adoption. Fathers generally have the right to stop a mother from giving up a child for an adoption, though the laws differ from state to state. You have the right to determine parentage of any child as soon as it is born, though the mother can choose to do anything she wants before then. Once the child is born, you have the right to ask for paternity testing and to establish your rights as a father. The adoption cannot proceed until you agree. You cannot stop any steps the mother takes before the birth, but the mother can't give up the child without the consent of the father.
Fathers have no rights over a woman's decision to abort a child. While various state laws impose specific requirements or restrictions on the abortion process, the father of an unborn child has no right to decide whether or not to proceed with an abortion.
The only right you have in the abortion process is in talking to the child's mother about the process. You cannot prevent or physically restrain the mother if she seeks an abortion, nor can you force the mother to get an abortion if she doesn't want one. Your only role in the abortion process is that of an adviser.
Paternity is the legal recognition that a man is a child's father. This is typically established at birth or sometime thereafter. However, advances in medical testing technology now make it possible for courts to determine paternity before birth. Paternity laws exist in every state and allow you to ask the court for an order to determine parentage. Court grant such requests when the father is unknown or when paternity is disputed, but typically only after the child is born. This doesn't mean you do not have the right to ask a court to order a paternity test for the unborn child, but it doesn't mean the court will grant your request either. In other words, you have the right to ask, but that's about it.