How do you file for sole custody if the other party is dangerous andinsists on seeingthe child?

There are two types of custody; physical custody and legal custody.  You have physical custody because your daughter lives with you.  Legal custody means making decisions about your daughter's healthcare, education, etc.  Visitation is a separate issue from custody.  Since your daughter is accustomed to living with you, and since she doesn't know her father and given his criminal record, a judge is NOT going to grant him physical custody.

Since neither you nor the father showed up in court, most likely the judge dismissed the petition for visitation.  You can check the court file to confirm what occurred at that proceeding. If you don't know the case number, obtain the case number from the court's computer by looking for your name or the father's name to find the case. Give the case number to the court clerk who will locate the file.  You can't remove the file from the court, but can look at it and request that it be photocopied by the court clerk.  Since you were not served and since the father has a warrant for his arrest, it is unlikely he will be pursuing visitation or custody.

You can file an Order to Show Cause (court form) requesting sole (legal) custody.  Attach a declaration signed under penalty of perjury stating the facts supporting your request for sole custody to the Order to Show Cause.  You should also attach a proof of service.  When you file your Order to Show Cause with the court, the court will set a date for a hearing.  You will need to serve the documents on the other parent.  You can use a court form proof of service or you can write your own.  If you write your own, it just says that you are over 18 and the attached documents were sent via first class mail unless specified otherwise to _________ (name and address of other parent) on ________ (date).  You sign and date at the bottom under penalty of perjury.  The date you sign should be the same as the date of mailing and the same date you file your documents with the court.

As for visitation, if the father pursues it which seems unlikely given his present situation, you might want to consider supervised visitation if he ever prevails on the visitation issue.  You also want to include in your court filing the fact that he hasn't paid child support.  He could be subject to civil or criminal penalties for failure to comply with a court order to pay child support.  Child support is a separate issue from a father's right to visitation.

If he poses an immediate danger, you might want to consider a restraining order.