There is no such thing as a web folder. In fact there are no files on the internet. All that exist are services.
Your iOS app can connect to services and consume whatever they provide. http doesn't provide a way to list files. ftp provides a way to ask an ftp server for a list of files. WebDAV is a service built on http that (I think) provides a way to list files. I believe that Apache, a web server, can provide a list of files in an html page. But it does so in a way that doesn't conform to any standard.
If you control the web site you could provide a file on the server that has the information that your app needs.
There is no simple solution to what you're asking.