A small text file that a web server stores on a user's hard drive when the user visits certain websites is called a

A cookie is a small text file a web server places on the user's hard drive to remember data between visits to a website.

The browsing history is a record of visited pages kept by the browser, not a file the server stores on the disk.

Logjam is the name of a cryptographic attack, not any stored text file.

Since cookie matches the description fully, none of the other entries can be right.

Cookies store items like login state, preferences and shopping cart contents.

They can be first party from the site itself or third party used for tracking.