I would definitely seek the advice of a family law attorney in your area. If you formally signed your parental rights away pursuant to a stepparent adoption, then generally your obligation to pay child support would end at that time, although you could still be liable for any unpaid back child support.
However, if you informally "signed away" your parental rights, i.e. signing something with the mother of your child, that alone will likely not be enough to terminate your legal obligation to support your child. Therefore, you need further legal consultation on this issue.
The law in Alabama used to be that having your parental rights terminated in a court order would also terminate your obligation to pay child support. However, due to a somewhat recent change in the law, a person whose parental rights have been terminated is now still obligated to pay child support. As another answer pointed out, an exception to this rule could occur if the child has been legally adopted by someone else, because at that point the child becomes that person's legal responsibility. But under current Alabama law, terminating parental rights does not terminate the obligation to pay child support.