Citing a work authored by “A. Smith with B. Jones” I have a book, for simplicity’s sake let’s say it’s written by “A. Smith with B. Jones”. Note the with, not and. This how the authorship is credited both on the cover and inside the book.

This is because one of the writers did by far the majority of the work. So, how should I cite it? I am considering the following options:


In-text citation:


  (Smith &amp; Jones, p. 11)  
  
  (Smith with Jones, p. 11)

Reference:


  Smith, A. &amp; B. Jones 2020. A book's title. Chicago: University of Chicago Press.  
  
  Smith A. with B. Jones 2020. A book's title. Chicago: University of Chicago Press.
The main point of citation style is to allow the reader to identify and find the work in question, not to please the authors, correctly represent their contributions in detail, or reproduce how the authors were listed on the publication in absolute detail.
In fact, hardly any publication has equal contributions.
Probably the only reason we do not see other conjunctions very often is that most citations are to papers where the journals control the style and nip any trend towards this in the bud.

On the other hand, the odd with may be confuse the reader. Consider:


  Smith with Jones (2020) established …  


As a reader, my first assumption would be that you made a mistake and I consider the following “corrections” equally likely:


  Smith &amp; Jones (2020) established …
  Smith (unknown year) with Jones (2020) established …


Hence: Ignore this peculiarity for citing. It does not hinder the reader to identify or find the paper. It is only confusing and unnecessarily complicates things. 

Some illustrative examples leading the alternative ad absurdum:


In a paper with alphabetical author ordering, you do not try to figure out who contributed most and name them when citing. Not only would this often be unfeasible if not impossible to find out, it would also strongly harm the identifiability and searchability of your reference. Aaronson’s contribution to “Aaronson et al.” may be minor; they were just the first in the alphabet.
If a paper has co-first-authorship (“these authors contributed equally”) and further authors, you still cite it by only naming the original first author. Taylor may be a co-first author with Williams on “Taylor et al.”.
You can imagine arbitrary complex authorship phrases. Would you honour the following?


  A. Smith together with B. Jones and some contributions of C. Taylor as well as a chapter by D. Williams

Depending on the journal’s style, a paper by the same group of authors may list them as:


  A. Smith, B. Jones, C. Taylor, and D. Williams
  A. SMITH¹, B. JONES¹², C. TAYLOR³⁴, D. WILLIAMS¹⁵⁶
  A. Sᴍɪᴛʜ*, B. Jᴏɴᴇs†, C. Tᴀʏʟᴏʀ§, &amp; D. Wɪʟʟɪᴀᴍs♠ [sorry for Unicode abuse]


This should not affect your citation the slightest.


The only exception I can think of is if you are Jones and this is your CV, which should humbly reflect that your contribution was only minor.