If you and the Father are unmarried and there has never been a court order entered addressing co-parenting, you have sole custody of your son. As the sole custodian of the child, you get decide what contact, if any the Father has with your son. With regard to threats by the Father, if the Father is threatening you with violence or is stalking you in some way, you should seek an order of protection against him. However, if the Father is merely threatening to bring legal action against you, would not be entitled to obtain an order of protection against him on that basis. So the nature of the threat is something that needs to be known in order to give you guidance on how to address it.
With all of that said, the Father may file a petition seeking co-parenting time with your son, and the Court will make a determination as to what co-parenting time he should have (if any) based on the factors set forth in Tenn. Code Ann. § 36-6-106(a)(1)-(15). Unless the Father (or his significant other if she is living with him) is using illegal drugs, is abusing alcohol or driving under the influence of alcohol with the child in the vehicle, engaged in illegal behavior, engaged in a relationship where domestic violence is occurring, is a convicted sex offender, has abused this child, or has a history with the Department of Children's Services, the Court is likely to award him some co-parenting time if he . You should be aware that one of the factors considered when determining a co-parenting schedule is "the willingness and ability of each of the parents and caregivers to facilitate and encourage a close and continuing parent-child relationship between the child and both of the child's parents, consistent with the best interest of the child."
I would recommend discussing the particular facts of your case with an attorney. If you get served with a petition by the Father, you should obviously hire an attorney to represent you in the matter as soon as possible.
