There is no context as such except for sa inside the DB engine.
Based on your recent questions, you mean external SQL Server context which will be the service account used (you can see it in Services.msc). So if you are using domain\Specialuser
then you could permission domain\Specialuser
on a folder.
However, SQL Server 2005 introduced some groups that should contain the service account specified at install time and these should be used for external (eg outside SQL Server) permissions
Some details in KB 283811 , but best seeing "Reviewing Windows NT Rights and Privileges Granted for SQL Server Service Accounts". The groups mentioned here are what you should permission on your desired folder.