I got an error message, connecting via https to my owncloud server using DAVdroid.
„…2016-05-16 09:03:10 4 [ui.setup.DavResourceFinder] PROPFIND/OPTIONS on user-given URL failed EXCEPTION javax.net.ssl.SSLHandshakeException: javax.net.ssl.SSLProtocolException: SSL handshake aborted: ssl=0x7c4a4420: Failure in SSL library, usually a protocol error error:1407743E:SSL routines:SSL23_GET_SERVER_HELLO:tlsv1 alert inappropriate fallback (external/openssl/ssl/s23_clnt.c:744 0x7a359894:0x00000000)…”
I use a mobile phone with Android 4.4.4.
After updating owncloud to 9.02 I had still the same problem. I asked my webspace hoster (webspace4all.de) and got the answer that they only support TLS 1.2 from now for security reasons. This is a general advise what you surely know.
However in Android below 5.0 (and up 4.1) TLS 1.2 is implemented but deactivated. http://blog.dev-area.net/2015/08/13/android-4-1-enable-tls-1-1-and-tls-1-2/
I don't know how to activate TLS 1.2 in general but the link above describes a function to access TLS 1.2 by the apps! I think.
Can you update the DAVdroid to use TLS 1.2 with KitKat?
32.5% of all devices using KitKat https://en.wikipedia.org/wiki/Android_version_history