I have created a Debian package and now I want to release it somewhere and maintain versions and releases. Once every new release is thrown it should notify initially about the new version and auto-update.
"Release it somewhere" is what distros do.
- See http://mentors.debian.net for how to get it into Debian. It will then flow downstream into Debian-based distros like Ubuntu.
"Once every new release is thrown it should notify initially about the new version and auto-update" is a problem. That happens to be quite the opposite of how Debian likes to handle new versions...
- In Debian-based systems, you dist-upgrade the entire OS and all applications at once (Ubuntu calls this a release-upgrade, like 20.04 to 20.10). There are very good reasons for this behavior: A uniform set of packages requires fewer volunteers to test and support.
- Many Debian Developers tend to be very much against unnecessary user notifications, unnecessary out-of-band upgrades, and third-party non-Debian self-upgraders. It's rather viewed as re-inventing your own wheel, but somewhat less round than the original. Be aware that a Debian maintainer might remove your auto-update feature so your application behaves as Debian users expect.
...but auto-updates are normal behavior for snap packages.
- Snap packages are not debs. A snap includes it's dependencies and auto-updates frequently (often without user notification). Snaps are distributed through the snap store.