Moodle normally redirect to login page when session Timeout.
Is there any option to redirect another page url instead of going to
$CFG->wwwroot.'/login/index.php'
You can override the default login page by setting $CFG->alternateloginurl
via the admin interface at /admin/settings.php?section=manageauths
. Any redirects requiring user login will then automatically point to your custom location instead.