Is there a fee for processing an Application for Authority to Solemnize Marriages?

Yes.  Effective July 1, 2019 there is a $30 fee for all Applications.  In addition, background checks are performed on all applicants, with the exception of single ceremony applicants and U.S. Armed Forces Chaplains.  The fee for the background check is $54 which goes to the third-party vendor conducting the investigation.  Details regarding payment of these fees are included in the application instructions.