My ex boyfriend walked out on me while I was pregnant amd he was depolyed out of the us when our daughter was born so he is not on the birth certificate when he returned to the us and Ive tried multiple times to get him to go and take a paternity test but he would always refuse that she was his and disappear and he has never tried to have any contact with me or her at all (our dughter is 5 years old) then after all these years I've been able to find him on Facebook through his new wife's page and start the child support process and I'm getting dna tests done... now that I'm filing for child support against him for daughter he and his new wife are threatening me that they are going to try to get partial custody of her.. Is there any way of filing for abandonment against him so that he won't be able to get partial custody since he hasn't tried to have any contact or giving any kind of support for over 5 years towards me or our daughter?

PLEASE SOMEONE GIVE ME SOME ADVISE

No,

You have not really "tried" to get a paternity test, since you never went to court, just asking him to do one is not trying to make him. The only way to make him is though a court order.

In most places he does not even owe support since you have never went to get a court order for support.

He is also not proven the father, so that has to be proven before anything else happens

The threats of taking custody is just that, I would have been surprised if he had not said that
Most likely next he may threaten hard to you or threaten that you will never see child again. This is just normal threats.