Filter by API to nested field

I want to perform a filter using the API to get all the items in my “customers” collection where I have the “books” field. In this collection I have a “set of fields” type field called “publisher” with a field called “date”.

I would like to get all the customers who have books from publishers with the existing date value $exists.

https://api.mycockpit.com/api/content/items/customers?filter={“$and”:[{“_state”:1}]}

How would the filter be performed with that type of nesting?

If I can’t filter I will have to create those fields outside the “set of fields” but that would really be a lot of work :confused:

Currently this is the link I have:
https://api.mycockpit.com/api/content/items/tickets?filter={“$and”:[{“_state”:1},{“owner.customer.email”:“me@gmail.com”}]}