This praticular one is from Podjelje v Bohinju. Historically these types of "hats" were present in much of Slovene territory or at least alpine and pre-alpine areas but its true only in Zilja they still use them. They are/were often worn under hats.

I know, but I couldn't find any better picture, so I used this one. It's basically the same, so … Actually these caps were worn beneath hats. I'd like to have such one. They look awesome. A pitty they aren't worn anymore with our costumes (exremely rare). :(