In a gingerbread man scary story, what makes him scary could be his desperation. He is constantly running for his life, and this sense of panic and fear is quite eerie. For example, when he is being chased by various predators like the fox or the old couple, his frantic running and the idea that he might be caught at any moment creates a sense of dread.
The muffin man is scary because of the rumors surrounding him. There are stories about people disappearing after going into his bakery, and the strange noises that come from it at night. Also, the fact that he seems so isolated and his muffins have an almost hypnotic allure that might be hiding something more sinister.
I don't really know specific 'Jangly Man' scary stories off the top of my head. But perhaps it could be a creepy figure that lurks in the shadows. Maybe it makes a jangling noise as it moves, like chains or old keys. It could be that it haunts an old abandoned house, and those who enter at night hear the jangling and see a tall, shadowy figure approaching.
His appearance. Being a little green man is not something normal. The green color, which is not common for humans, gives an otherworldly and spooky feel. And if he has strange features like big eyes or sharp claws, it makes him look even scarier.
Maybe it's the fact that a lollipop man, who is usually associated with safety and helping kids cross the road, becomes something menacing. It's a subversion of the normal, friendly image we have of them.
The noise he makes. The jangling sound is often associated with something strange or out of place. It could be a warning sign that something bad is about to happen.