NM Law - Abandonment/Child Support/Fraud

Am I able to file for abandonment in NM?

Father has not been in childs life, left
the state and don't know where he is. He had visitations but didn't use them.

Hasn't paid child support in over 4 years and before that it wasn't even for 6 months.

Bench warrent was put out for him several years back for not following what the judge had asked reguarding getting a job and paying child support.

Found out that a couple of months ago he opened SEVERAL credit cards under my name and has given me bad credit by not paying them. These are the only ones I know of. Fraud charges have been filed.

I have spent money in the past for attorneys but will never get the money back from him since he leaves, doesn't have a job or some other reason.

NEVER have I spoke ill of him to or around my child. He doesn't know him and doesn't even ask about him or anything like that.

I'm worried if something shall happen to me that I wouldn't be able to protect my child and have him taken care of by my family.

Please help me...Thanks in advance...