Foreigner Unwed Father to a U.S. Citizen Child

My question involves a child custody case from the State of: TN, I am a not a citizen of US and my partner is a US citizen. She filed a divorce against her husband and they settled. The custody goes to the father. In the meantime, (and please do not redicule me) My partner and I had a son. I support them and sent them money every two weeks about $400 a week. I even visted the US and stayed for three months. We were under the understanding that as soon as the divorce is finish we will get married so she can come to my home country or she can petition me. Shortly after my return here in my home country she started complaining and started fault finding me. In short she wanted to end our relationship and I have a feeling that she will reconcle with her estranged husband and take my son with her.

My name is in the birth certificate and I am also organisng a DNA test to establish my paternity.

My question is, is there a way I can get my son... My issue is my partner could not find a job and not capable of raising our child and to make it simpler for her she is dumping me.

Why is she not capable of raising the child?

A US court is very unlikely to send a US citizen child out the country to live. The gov't is not going to give you immigration status to raise a US child here.

You can litigate child custody in the state in which the child is domiciled. You should expect that you will have to be present in the United States at times during that process and, realistically speaking, should hire a family lawyer to represent you in court. It's not enough to claim that your ex- is "not capable of raising our child" - if you want to try to convince a court of that you will need to prove that the person you chose to entrust with the continuing, sole custody of your child when you left the U.S. is not a competent or approrpriate custodian.