We've a use case where our customer wants us to link a File record to Case but not fetch it via Content Document link API call i.e. mark it private for selective internal Salesforce users. In nutshell, is it possible to have privacy settings specific to user on Files linked to Case records?
You can use the ShareType field on ContentDocumentLink to control the access to file.
Additionally, you can move your files from Case to a Child Custom Object and control access of files using the record access on this child object records.
You would have to write trigger on ContentDocumentLink to update access and moving file to child object.