Hi, Aisaki, this is A. Lawliet, the writer of Death Note: The Next Kira. As I stated before in the comments on Death Note: Hayden, it'll be fine if you wanna read the prequels before the actual story.
Also, the story of Death Note: The Next Kira is going under high maintenance. I'm currently changing some arcs after I went back and forth with stuff back when I first wrote Death Note: The Next Kira.
Now that I know which path to take, I will make some changes to fit the story I went for. And add some things that were supposed to be in the story, but didn't end up making it. ^_^
