Yes, there are likely to be some. Fanfiction is a vast world and many creative writers combine different fictional universes like Harry Potter and Norse mythology. You can try searching on popular fanfiction websites such as Archive of Our Own or Fanfiction.net.
The fanfiction 'Laufey's Legacy: Loki's Childhood' is quite good. It portrays Laufey as a complex figure in Loki's life. It shows the good and the bad aspects of his parenting. Another notable one is 'Baby Loki's World with Laufey' which creates an immersive world for the two characters. It has a great plot that keeps you engaged as it unfolds the story of their relationship.
It could be about various things. Maybe it's a fan - created story where Loki has a baby, perhaps exploring how he deals with fatherhood, or it could be about the adventures that involve Loki's baby in a fictional universe full of magic and mystery.
One possible plot could be that Loki, reincarnated in the Harry Potter world, is initially confused by his new surroundings. He then discovers that his powers are still there but manifest in different ways in the wizarding world. He might get involved in the fight against Voldemort, not because he's on the side of good, but because he sees an opportunity for chaos and power. Along the way, he forms unlikely alliances with some of the Hogwarts students, who are both intrigued and wary of him. And his presence might also disrupt the normal order of the wizarding world, causing new problems and solutions to emerge.
One popular baby Loki fanfiction might be those that explore his early life in Asgard. For example, stories could focus on his relationship with his mother Frigga. Maybe she's teaching him magic in a tender moment, and the story delves into how that shapes his character later on.
Some 'baby Loki fanfic' could be about his magical training as a youngster. In these stories, Loki is shown to be a quick learner but also facing difficulties due to his mischievous nature. He might accidentally cause some chaos during his lessons, which makes for an interesting read.
A very frequent theme is the comical aspect. The contrast between Thor's seriousness and baby Loki's mischievousness leads to many humorous situations. For instance, baby Loki might steal Thor's food or use his limited magic to play tricks on Thor, like changing his hair color.
One common theme is the adjustment to parenthood. Both Loki, with his complex past and powers, and Darcy, with her own unique personality, have to adapt to taking care of a new life. For example, in many stories, Loki has to learn to control his temper around the baby.
Well, Loki is obviously one of the main characters. And then there's often the baby, who could be an original character created just for the fanfiction. Sometimes, other characters from the Marvel universe like Thor or Odin might also make an appearance to interact with Loki and the baby.