I have refused to keep my child. She is 15 years old. My ex-husband went to court and got some kind of court orders for me to have visitation. The orders state that I was sent a letter for this hearing I never received such a letter. Do I have to follow these orders to visit my child if I do not wish too or can I relinquish my parental rights?

Failure to perform what is ordered in a court order can give your ex grounds to hold you in contempt. Have you read the order? Have you been ordered to pay child support?

I dobt the court has "ordered" you to vist, but that the court has allowed you a time to visit. Normally you are not required to visit during your visit times, but failure to do so, can normally allow the child's custodial parent to use this against you. You most likely can not sign over your rights, It sounds like he went to court to get custody, and to get child support ordered, You will have to pay the ordered child support

The courts don't "order" you to visit. As Chuck said, they have ordered that you be allowed certain times to visit. You don't have to exercise those rights if you don't want to (although I don't know who wouldn't want to be with their child).
You will most likely be ordered to pay child support as well... that, you DO have to do regardless if you choose to see your child or not... you are still responsible for supporting them.
You cannot relinquish your parental rights unless the father is in agreement and has a current spouse that is willing to adopt the child in your place.