This is what you need to do to be able to create Issues with custom fields:
1) First find out what JIRA keys your installation uses for the custom fields you want to use. For instance the custom field Epic Name is mandatory for Epics but has different keys depending on the environment. Use Postman or SoapUI to find out what these fields are with the url below for JIRA Cloud installations. Don't forget to configure basic authentication of course.
In my case I am interested in a couple of custom fields:
2) Add each custom field as a Text attribute to the IssueFields structure in JIRAConnector