Are there any countries in which banks do not need to follow any special regulation other than the regular business regulations. If not, are there any countries that come close? For more information https://en.wikipedia.org/wiki/Free_banking?wprov=sfla1 .
I'm going to stick my neck out and say that the answer is no, not because I have a specific reference (people tend not to publish papers stating that something doesn't exist) but monetary systems has been a keen interest of mine for the past decade and if free banking was currently being practised somewhere I would almost certainly know about it.
It has however been practised historically, perhaps most notably in Scotland 1716 - 1845.
You can find many proponents of free banking in the Austrian School of economics, for example George Selgin.