On this website, I've a Popup plugin installed (Layered Popups) that will be displayed "Once per session".
But how can I define the Session expire time?
If the plugin does not have a user interface to make adjustments in the backend, you would probably have to edit the plugin code to change the session parameters defined the the plugin author. This is not recommended because if you upgrade the plugin, you would lose those changes.
The PHP session time are set in your PHP config.
This answer here most probably will answer your question in detail. I dont know how to mark a question as a duplicate, if I knew I would have: How to change the session timeout in PHP?