And now you want to know what your RIGHTS are?
How about learning what your RESPONSIBILITIES are? Whether you are on the deat beat dad list or not, you ARE a deadbeat, though you have yet to prove that you are a dad.
It's sad that it took your girlfriend to make you see that. But at least you are now looking into your child's needs. You should try to find your child and sincerely apologize to the mother for your absence. Be ready to set up a child support plan and ask for times that you can see your child. Offer to help in whatever way you can.
Those are just the beginning of your responsibilities. It is far too soon to begin discussing your "rights". You should be thinking about your child's rights. You have a lot of redemption ahead of you before you start asserting rights.