Shortened term for “No Magic” – American Wizarding slang for Muggles, or non-magical humans (Pm).
First revealed in promotional materials for the movie Fantastic Beasts and Where to Find Them.
In an essay entitled Did J.K. Rowling make a muggle mistake by inventing an American word? fan Chris Taylor discusses the fact that many American fans were not thrilled with the phrase "No-Maj" being used instead of the well-known "Muggle"
The problem with "no-maj," the real reason why it has provoked widespread outrage on Twitter, is that it doesn't sound particularly American. Perhaps it's supposed to invoke a product name like the caffeine tablet "NoDoz"; perhaps it's along the lines of the little-used alternate name for midges, "no-see-ums." Either way, it comes across as pretty condescending — like all Americans are obsessed with marketing or speak in some kind of weird local dialect.