It focuses on the story of L's early days and how he solves cases. In this novel, we see L's unique detective methods and his battle of wits against various criminals.
There are many good ones. Some fanfictions expand on the backstories of the characters. For instance, there are stories about how Ryuk came to be the Shinigami he is. These can add a whole new layer of understanding to the Death Note universe. You should explore different tags and categories on platforms like AO3 to discover such great fanfictions.
One possible fanfiction could be where Light is in the hospital due to an unexpected illness. Maybe he uses this time to plot his next moves in the Death Note world without arousing too much suspicion. He could be pretending to be weaker than he actually is while observing the people around him, looking for potential Kira supporters or enemies among the hospital staff and patients.
A really good Death Note fanfiction is 'The Death Note's Origins'. It goes deep into the creation of the Death Note and the backstory of the Shinigami world. 'Ryuk's New Game' is also cool, where Ryuk decides to start a new kind of 'game' with the humans. 'Near's Ascent' is interesting as it follows Near's journey to become an even greater detective than L, with some new challenges and plot twists along the way.
There are several places. Fanfiction.net is a popular website where you can find a large amount of Death Note fanfiction. Archive of Our Own (AO3) is also a great option. It has a well - organized tagging system which makes it easy to search for specific types of Death Note fanfiction, whether it's about certain characters or particular plotlines. Another place could be Wattpad, though the quality and variety might be a bit different compared to the other two.