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 tier (always mindful that the higher tiers have access to the lower tiers). They will all be available via the same feed. If their pledge becomes inactive, the feed stops working, but it will become active again when the patron renews the pledge.
The RSS feature on Patreon is meant to offer patrons the ability to listen to a supported creator's audio podcast while using their favorite podcast app. This makes it easier for them to enjoy the content while not having to log in to Patreon through our app or mobile web. That being said, sharing a custom RSS link with other users on purpose, (and giving them free access to patron-only content) is a violation of our terms of service.
For more information, check out this helpful article, and stay tuned to hear how creators with podcasts are having success on Patreon.