I would like to point out that by doing some casual searching on Google, it appears that using Patreon as a writer seems to not be an issue with Copyrights. Since people are not purchasing your book, they are instead donating to you as an Artist, it should be okay.
If, on the other hand, you are planning to actually publish the story and people purchase it, say like on Kindle, then you can't do that with fan fiction.
I am not a Lawyer, so this isn't legal advise by any means.