Your list of custom fields as well as the list within the "custom fields" panel in your individual supporter profiles is displayed in order of the "order" value first, then in alphabetical order. An Order value of 0 will list above 1.
The Order value can be set individually through editing custom fields here:
but if you want to batch update your custom fields, this can be done through an import.
To assist with an import, you'll first want to create a custom report returning at least the custom_column_KEY and Order fields from your custom fields. (Just email firstname.lastname@example.org if you need assistance with this.)
You can then export those report results, update the order values as preferred, and re-import to a write-in table of:
making sure to match the custom_column_KEY and Order values so that the existing custom fields update as intended.
Your custom fields will also display in this order on your public pages, so if you select three custom fields for a specific signup page, those three fields will display in ascending numerical order on the signup page as well.