Yes! You can protect folders but not individual files. So, if want to limit access to a file or set of files, they need to be in their own folder.
Access your cPanel. In the Security section, click on Password Protect Directories.
Click on the Video Tutorial link at the top of the page for a demo of how this works. There are two parts, so don't forget to create at least one user. You can give several people the same access information, or you can create a separate username and password for each person.
Navigate to the folder you want to protect by clicking on the folder icons. Click the name of the folder to add protection. In the field that says, "Name the protected directory:" you can write something like "Private" or "Temporarily Unavailable." This is the message that users will see, along with a User Name and Password box.