You can require existing fields but if you have custom patron attribute types, you have no way of making them required, thus they are not added with the quick add new patron function.
I think this is a duplicate, but in current versions the patron attributes can be marked required.
(In reply to Katrin Fischer from comment #1) > I think this is a duplicate, but in current versions the patron attributes > can be marked required. Hm, need to confirm for quick add tho!
I just tested this on 21.05: If you mark a patron attribute as mandatory, it will show up on the quick add patron form.