How can I change the order in which Categories or Category Options such as Year, display in the drawer?

The order in which Categories (as well as Tags, Keywords and Job selections) display in the Filing section of the drawer is controlled by the order in which they are saved for the specific Cabinet.

The order in which the Options for a Category display in the Filing section of the drawer is controlled by the order in which they are saved for the specific Category.

These can be changed by an FYI Admin in the Cabinets and Categories. Refer to:

Changing the Order in which Categories, Tags, Job and Keywords Display in the Drawer in Managing Cabinets
and
Changing the Order in which Options Display in the Drawer in Managing Categories.