You need to remember that you chose this man to be the father of your child. It's too late to "unring that bell". Bio-Dad has constitutional rights to have a relationship with his child unless he is proven to be "unfit". Being unfit is not the same as you thinking he is lousy father material. He does not have to exercise those rights, but he does have rights.
The likelihood of him getting custody is remote. The likelihood of him getting visitations, however, is good.
Child support and visitation are separate issues. If he is not paying child support, you seek enforcement either thru the Child Support Enforcement agency or thru the courts.
If he has not seen his child in a couple of years, you certainly can ask that his initial visitations be supervised. But, supervised visitations generally do not last very long. However, some men and women when confronted with the notion of supervised visitations, will not bother to show up. If he does not, then it is unlikely that the visitations will progress to unsupervised.
Discuss it with the attorney you consult, but be prepared to hear that you cannot totally exclude bio-Dad from the life of your child if he insists upon exercising his constitutional rights.