The Jersey Devil legend is more well-known by people who grew up in New Jersey, as opposed to transplants from somewhere else. The reason for this is because children at a young age passed on the story throughout the years. The legend is extremely old and details get changed from time to time. Some believe that the Jersey Devil started out as a ghost story told to children.
A couple hundred years ago, people didn’t have as much to occupy their time besides working and reading. Ghost stories were extremely popular among the youth. Parents would warn the children that if they didn’t behave and lived a sinful lifestyle, the Jersey Devil would fly into their window at night, take them out of their beds and fly away with them. (I know that’s kind of sick to tell a young child that, but probably also very effective.)
So the children would learn of the monster at a young age. They would pass the story to their friends and most-likely elaborate some details. The legend has lasted over the years mainly because of young children’s imagination and of course, the fact that the Jersey Devil is real.