Use No Stored Cookies

We’re new here so if this is the wrong place, please point us in the right direction. Thanks.

We have a “Members Only” section that requires a password to enter. This function currently requires the users browser to accept stored cookies. We can not allow stored cookies to be saved on the computers our members use. Session cookies would be fine but not stored cookies. I have not found anything that allows us to change the type of cookies used. Where is this function being done and how do we not allow any stored cookies? Thanks for your help!