First, you need to know both universes well. Read the books and watch the shows. Then, create a unique concept that combines the two. For example, a story about a vampire from Twilight falling in love with a werewolf from The Originals.
Character development is key. You can't just rely on the existing characters' personalities. Give them new traits based on the new situation in your fanfiction. Also, build a strong plot. Maybe a mystery that involves both Twilight and Originals elements, like a powerful artifact that can change the fate of both worlds.
When writing a 'Twilight and Originals Fanfiction', don't be afraid to deviate from the original canon a bit. But also, keep the essence of the characters. Use vivid descriptions to bring the settings of both worlds to life, whether it's the gloomy Forks from Twilight or the supernatural - filled New Orleans from The Originals.