To add custom fields to branches, log in as administrator to your system and from your Administration dashboard visit the Extend Profile section. Over there you shall find a tabular list of all your defined Extended Profile Fields. To add a new profile field click on the button "Add Field" on the top left corner of the screen (1).
Fill in the field properties, such Name, Label, etc and for the option Create for choose Branches (2).
Once you have created your new custom field for courses, it will appear in the list of all available extended profile fields.
Later, when you add or edit a branch this field will appear among the branch settings (3).