I have a Patron-only feature where I post a chapter of my book series each month. At the top, I link to the beginning of the series. At the bottom of each chapter I link to the next one when it’s posted.
Not sure if that was what you had in mind, but it’s certainly not necessary to shell out for another website/blog in order to post a series.
Author Tobias Buckell has a “Table of Contents” where he has links to all his Patreon stories (and he has A LOT of them), which I think is a tidy way to do it.
Now I also have a similar TOC but this links to BookFunnel copies of my books (another Patron-only perk) in which only active Patrons can download my books (easy to set up).
Hope that helps!