This depends on what kind of fantasy or mystery you are interested in. A lot of paranormal or thrill seeking kinds are very popular, but can cause a lot of writers block. Sometimes, you can begin a book almost like a normal book, and then surprising put in something unexpected, like a character dies or a huge event that was not expected comes up. You could also begin with a sudden jump start. Like someone is screaming. It really draws in the reader's interest. I hope this helps! I'd love to help you, if you have any more questions please ask.