How can I have my fiance listed as my son's father in the birth certificate?

You will want to make sure that the divorce court in Utah shows that there is another child born to you which is not a child of the marriage. You can go to the Bureau of Vital Statistics in the state where the child was born and either apply for a birth certificate, if one has not been issued, or to amend a birth record, if a birth certificate has already been issued. You and the father can sign an affidavit with the information necessary to have a birth certificate issued or to amend a birth record. If your husband is claiming to be the father of the child, you will need to contest that in the divorce and ask the court for paternity testing to establish that your husband is not the father of the child in question, and that your boyfriend is the biological father.