If you don't want to store data on users then you will have to use existing data they already have: browser version, IP, user agent... but that's not going to be very reliable, cause any website will be able to see that information, and thus the session will be insecure.
That doesn't happen with cookies, cause they are "private", they can only be seen under a certain domain.
Another method as you know is adding a secret tag in every html link/form your server generates, and use that secret key to identify logged in users.
That's similar to cookies, but more complex. You don't have to "store" anything on user's machine...
There is a problem with this method, if the user shares a link, a custom link, then your secret key won't be secret anymore.
EDIT: I've found a similar question you should read Node.JS session without cookies