Can I add a custom priority or other custom field to a Story, Epic, or Milestone?

Not for now. We've found that custom fields have the ability to cause users more problems than they solve, but we are tracking this request internally. 

Currently, priorities in Clubhouse are structured vertically in a workflow state column. The higher up in the column the Story, the higher its priority. By default, newly created Stories populate at the bottom of their assigned workflow state column, and they can be dragged up or down to change their priority.  

What we often recommend to Organizations, in tandem with our default priority system, is to use Labels (or for Milestones, Categories) to show or manage custom priorities on Stories and Epics. For instance, at Clubhouse, we use severity labels to denote how urgent a reported or internally found bug is.

Although Milestone categories are used to make grouping and filtering Milestones easier, the benefit to using labels on Stories and Epics is that
each label has its own page and reporting in Clubhouse. You and your team can see all Stories and Epics with that label and track progress on them as well. Clubhouse also has Quick Filters and Spaces on the Stories page, which allows you to zero in to labeled Stories fast and easily.