I have had sole and legal custody of my son his entire life and now his father wants joint custody. What are my rights. I have tried in the past to let my son see his father but stopped after his father tried to keep him in Arizona and said that he would not return him. The police were involved in retrieving my son.

He has also only seen his son a handful of times in 5 years. And only pays his child support when he has to in order to keep from going to jail.

You said what you rights are, you have sole legal custody. The question is not what rights you have but what rights he has. At this point he has none. But that doesn't mean he can't go to court to get rights.

On the other hand with a previous incident of parental kidnapping, I would say it would be very unlikely for a judge to allow anything more than limited supervised visitation.

No charges were actually filed. The police from Michigan contacted the Police from Arizona and when I arrived in Arizona the police went to his house retrieved my son and had me then come over to the house to pick him up. Should I file charges? This was 3 years ago.

Its too late to file charges, but you should get a copy of the police report of the incident if he does go to court.

I have had sole and legal custody of my son his entire life and now his father wants joint custody. what are my rights. I have tried in the past to let my son see his father but stopped after his father tried to keep him in Arizona and said that he would not return him. The police were involved in retrieving my son.

Do you have a court order awarding you "sole and legal custody"? From Michigan or Arizona?

The issue here is that unless the court took away his rights to visit, he may even still have them, was there a child visitation order in place

Sole custody does not mean he does not have visitation rights, those can be supervised or controlled and limited.

But he has the right to take you back to court like this, He will have a up hill battle with what little info you have provided but it is not unheard of