As of April 2017, Screens doesn't yet support authentication against system user accounts on non-Macs. That is to say, you can't use, for example, your Linux system log-in credentials in Screens as you can with a Mac (using the Mac User authentication method). The authentication credentials configured in the remote VNC server settings must be used.
If you experience an unsupported authentication method error when attempting to connect to a non-Mac, the destination computer's VNC server is likely configured with the Unix Password authentication option. Set it to VNC Password instead.