If you want the folder to be accessible to only one person (or a few persons), please use the share feature, not the publish feature.

If you want to share with different people and set different access permissions, then please use DriveHQ Group Account service. With DriveHQ group account service, you can create different sub-users; you can create different folders in your own account and share different folders to different users. You can set different level access rights, including read-only and full access rights, etc.