I have an alleged son that I had two paternity test one says I am the father and one says there is no possible way that I am. I have not seen him since he was born and I want to relinquish my rights. Is this possible given that I have no contact with him or his mother?

First no, a certified lab will not come up with one yes and one know. Did you have one done in a professional lab in a lab approved by the court?
If not that is your first step.

Next no you can not give up your rights unless you prove you are not the father by an approved DNA test that is accepted in court.

You do not have to see the child, you don't have to visit, you just have to send the child support each month.

If you have read the nearly THOUSANDS of threads on this subject, you would know that this is nearly impossible.

Have a third test done by a reputable lab. If you aren't the father you have nothing to worry about. If you are, take responsibility for your actions. I'm sure the mother has no choice but to be responsible to the child, yet you opt for the easy way out.