First thing you need to do is install and activate the Restrict Author Posting plugin. Upon activation, you need to go to Users screen, and click on the edit link next to the user you want to restrict. On the user’s profile page, scroll down to the Restrict Author Post to a category section and select the category for the user to post into. If you want to remove the restriction from an author account, then visit their user profile again and scroll down to the Restrict Author Post to a category section and select “No Restrict” to remove the restriction.
If you want a video tutorial of this article, you can check this or read the full article at Restrict Authors to Specific Category in WordPress.