Permit only one role to download files
It's good you're using Private file system. That is one level of control you need to prevent the files from being freely downloaded.
Other levels of control are the Page (Views list), Node, and File fields.
You could create two different Views, one without the file field, and one with it, and use Role permissions on those pages. In this case you'd have to make nodes not accessible to all, which isn't fortunate if you want to control other types differently. There are modules, though, that you can use to set up different node type permissions.
But in your case I think it makes the most sense to have different File permissions. This way you don't have to duplicate Views or control node access.
You can do this with the Field Permissions module.
All can see the nodes and Views pages, but only special Roles will see the File field that has those special permissions.