Does my ex have an anitsocial narcissistic personality...

YOU dont have to deal with him at all.
Let your lawyer do it - or Family Court or Friend of the Court if you are in the USA. Ask for psychological evaluation for him if you think he will not be a positive influence on the child.
Don't talk to him about this - bring in the professional help.

Listen to Punkey! Great advice.

I am in the mental health professional. The symptoms you describe can be many things ranging from a mood disorder (bi-polar), intermittent explosive disorder, substance abuse, to yes cluster B personality disorders such as antisocial and NPD. Many of these things overlap. I am not diagnosing and this is not intended to be medical advice. See a professional in person. I suggest that you do a lot of research and prepare yourself for battle. These individuals typically exploit vague parenting agreements to torment the other parent. Do your research now.

Other than bringing in professional help - if it's lawful in your state, record all conversations with him (digital voice recorders, smart phone voice recorders, and if necessary video - but this can antagonise people further).

If you aren't allowed to use those methods (and even if you are) - ask to only communicate with you through writing - either text, or email. This of course does make some communication difficult, but on the very positive side, it allows you to have evidence of what you have talked about, and it usually means they won't be abusive (in writing).

Keep a diary. Don't make it about petty things, and don't try and guess his motivations in your diary - try and keep what is written objective. That's because if you use it as evidence, defence will pick apart a diary (if it's presented as evidence), attempting to paint the writer as petty & vindictive...anything to not look at the content...so the content has to be objective. How you felt can factual, what was done can be factual, but why he did what he did, and the intended consequences of his actions - are just a guess on your part (no matter how well you know him)

Take note that this is a 5 yr-old-post so if you're intending to help Jessica, you're a bit late to the party.

Adding to a five year old post...

A competent mental health professional would not make assumptions based on a few word written by one of the involved parties. Every ex-husband thinks their ex-wife has an antisocial narcissistic personality, and every ex-wife thinks their ex-husband has one.

The best thing for the children is to not have both sides preparing for battle. Battles hurt kids.

A competent mental health professional would counsel parents who are divorced to find the best way to put aside their accusations and recriminations to work together for the good of their children.

I hope that five years ago our OP found a way to do this.