One great King Edward Twilight fanfiction is 'The Twilight of King Edward's Reign'. It beautifully weaves the world of Twilight with a historical take on King Edward. It shows how the characters from Twilight might interact in a time period related to King Edward. The author does a great job of maintaining the essence of both the Twilight universe and the historical context.
I really liked 'King Edward's Twilight Encounter'. This fanfiction imagines a scenario where King Edward stumbles upon the Twilight world. It has some great character development, especially for King Edward as he adapts to this new and strange world full of vampires and werewolves. The writing style is engaging and it keeps you hooked from start to finish.