Is it possible to patent the way folder structure is represented on the screen. In what sense it is patentable since it does not fit into any category but Apple and Microsoft have parts of their interfaces patented (Apple's Coverflow, for example)?
The statuary classes are compositions of mater, machines, articles of manufacture, process and improvements on those. (35 U.S.C. 101 Inventions patentable) A computer programmed to do a particular thing can be seen as a machine. "A machine for displaying the contents of a flash drive. . .", for example.
A set of steps carried out by a program can be a process, also called a method. "A method of displaying information . . ." is a reasonable preamble to a claim. There is no question that this would be a method. There is a big question as to if it would be an "abstract" method, and as such not patentable subject matter by judicial precedents.
Is your way of displaying folder structure new and unobvious? That is a separate question.