The default character of invoking ssh escape sequence is '~' (from new line of course). Twice typing of such character send the escape character itself. In situations where several sequential connections to terminal (or to console, like Oracle Solaris Zone console via zlogin -C) are made, you should know one 'trick' to disconnect only from last connection made.
Let me explain below. Let's start with session A - a session of your local machine. Here B - proxy vpn machine, C - Solaris server, D - newly installed Oracle Solaris Zone, not configured yet.
A -- ssh_via_vpn_to_B --> B -- ssh_to_server_C --> C -- login_to_zone_console --> D
When you type exit ssh sequence '~.' you immediately close your first ssh session from A to B.In order to close only zlogin session and stay in session on server C, you should type '~~~.' Doing it you transmit escape character to the appropriate deeper session in your 'connection stack'. Take it in your mind.
P.S. this doesn't work when ssh jumping or configured ssh proxy connection is used.