Current DAVdroid versions require Android 4.4 or later. Older Android versions are not supported anymore, but can you use old DAVdroid versions which were compatible with Android <4.4. However, all DAVdroid versions require Android 4 or later.
Older DAVdroid versions work with Android <4.4, but there is no support and there won't be any updates, including security updates. We strongly recommend to update your Android device to Android 4.4 or later (maybe using a custom ROM) and use the latest version of DAVdroid.
If you really need to install an old version of DAVdroid, we recommend to install F-Droid and activate "F-Droid Archive" in the repositories (F-Droid / Settings / Repositories, see screenshot).
Then you can use an old version which is compatible with your device.
You may notice crashes and other misbehavior with latest formally compatible DAVdroid version because compatibility was not tested enough anymore. In this case, use an even older version, which should be compatible again.