You can host your patrons-only podcast with Patreon! Your Patreon page includes an option for an RSS feed that is available only to patrons.
Each patron has their own login information built into the feed so that it is possible to serve one set of episodes for each reward tier (always mindful that the higher tiers have access to the lower tiers). They will all be available via the same feed.
The RSS feed only contains audio posts. You can make as many other posts as you wish. Only the audio posts will show up in the RSS feed and be made available to podcast apps. Your patrons will need to come back to your Patreon page to see any other content you posted.
You do not need to host these files outside of Patreon! You can include your episodes in audio posts on your own Patreon page. Any setting you make regarding access to a post will be carried over into the RSS feed. If you make the audio post public (even though the feed is automatically patron only) the general public will be able to listen on your page or through the Patreon app.