My ex boyfriend is threatening to put a restraining order on me. He is not the Father of my child. Can this affect my current custody order?

It shouldn't unless the reason for the RO indicates you might be a danger to the child.

The RO I believe that he plans to file is for harassment. There should be no indication of danger to my own child. The "harassment" he is speaking of is text messages asking him to not file because I do not know if it would affect my custody or not. There has been nothing threatening in any of the messages.

He is talking about filing an RO for harassment which consists of text messages asking him not to file? The timeline doesn't make sense.

He is talking about filing an RO for harassment which consists of text messages asking him not to file? The timeline doesn't make sense.

He asked me to stop texting him and that if I continued to text that he would file an RO. I then text him after asking him not file. He is going to use those as part of his argument to file since I continued to text. My only concern though if he does file if it can affect my custody since he is NOT the Father to my child.

The father of your child can try to use it to show instability, but I doubt if that will fly.