Yes you can create cookies that can only be read on the server-side. These are called "HTTP Only" -cookies, as explained in other answers already
No, there is no way (I know of) to create "cookies" that can be read only on the client-side. Cookies are meant to facilitate client-server communication.
BUT, if you want something LIKE "client-only-cookies" there is a simple answer: Use "Local Storage".
Local Storage is actually syntactically simpler to use than cookies. A good simple summary of cookies vs. local storage can be found at:
A point: You might use cookies created in JavaScript to store GUI-related things you only need on the client-side. BUT the cookie is sent to the server for EVERY request made, it becomes part of the http-request headers thus making the request contain more data and thus slower to send.
If your page has 50 resources like images and css-files and scripts then the cookie is (typically) sent with each request. More on this in Does every web request send the browser cookies?
Local storage does not have those data-transfer related disadvantages, it sends no data. It is great.