If ssh is able to establish the connection, it will set
DISPLAY to the proper value. Since you have
X11DisplayOffset set to 10 (the default value), ssh will use the first available display starting at 10. If you see a value that's lower than 10¹, then something is interfering with the normal X11 forwarding set up by ssh, at least by overriding
DISPLAY. The value
:0.0, the part after the dot is irrelevant) indicates the first display that was started on the machine, which in typical cases is the active session (or the graphical login prompt) on the machine's console.
The most likely explanation for the behavior you observe is that one of your shell configuration files sets
DISPLAY. The most obvious culprit is
~/.bashrc (which due to a quirk of bash is executed whenever the parent of bash is
sshd, even if the shell is not interactive). Another file that defines environment variables is
/etc/environment. If that's the case, the solution is obvious: don't set
DISPLAY there. (There are very few cases where you need to set
There are other exotic explanations. This might happen if you've changed your login shell to
screen (a cute idea in theory, but not practical) and you have a shell initialization file that forcibly sets
DISPLAY inside screen (not such a good idea). This could also happen if you configured the server to accept environment variables sent by the client (
AcceptEnv directive in
sshd_config), the client is sending
DISPLAY, and the X connection couldn't be established. Or it could happen if you set an environment variable on the server via the
command directive in
xterm could be a script.
¹ Or whatever the value of
X11DisplayOffset is in the server configuration, but it's hardly ever changed from the default.