Newfangled means new and perhaps needlessly modern. It may sound like a new coinage, but in fact fangel is an Old English word, meaning to take, and newfangled is not newfangled at all. It first appeared in the 12th century as an adjective describing a person overinterested in new things. It appeared intermittently in this sense before taking its modern definition by the early 19th century.
Newfangled is often unnecessarily hyphenated—new-fangled—especially, it seems, in British publications. But the unhyphenated form was established long ago, and there’s no reason to regress.
Fangled on its own is an archaic word. In modern sources, the only examples of fangled we could find appear in the phrase old-fangled, an interesting coinage obviously meant as an antonym of newfangled.
Examples
These newfangled machines tend to cost more than most kids’ bikes and scooters. [Washington Post]
Resisting a newfangled term, for example, can be a way of resisting the thing it denotes. [Telegraph]
Every second company said it was spesh because it had got one of those newfangled website thingies. [New Zealand Herald]