In order to give up your rights, you'd first need to establish that you had any, which would require you and the child to submit to a DNA test. If you are not sure that the child is yours, I'd find out before going through any legal process of giving up your rights.
If the child is yours and you do not wish to support it or be involved in the child's life, you can voluntarily terminate your parental rights
, once it's been established that you have any. OR she can petition the court to terminate your rights based on a set of factors that MS law lays out. If you do not voluntarily terminate your rights, she would have to bring the case for involuntarily terminating your rights. In either case, the termination would need to be approved by a Judge. Whether or not a Judge will approve it will depend on the circumstances, as Judges expect that two parents will support the child. In other words, the Judge may expect that you take responsibility for the child whether or not you want to.
I know right now you are not ready and do not want to deal with the mother
, but keep in mind that later on down the road, if you decide you want to seek out the child that bears your genes and DNA, if you have terminated your rights, you will have no legal right to see your child. It's a big decision to make, since you will be essentially rendering your child fatherless.