Yes, there are quite a few. You can start by looking on fanfiction websites like Archive of Our Own. Some fanfics might explore a deeper emotional bond between Harry and Hedwig that could be seen as a form of 'romance' in the sense of a very close, affectionate relationship.
In Harry and Hedwig romance fanfiction, the theme of companionship is quite common. Hedwig is Harry's constant companion, and writers may expand on this to show a more romantic - style relationship. Also, the idea of understanding without words is often explored. Since Hedwig can't talk like a human, their unspoken connection can be a key theme in these fanfictions.
In most of the original 'Harry Potter' series, Hedwig is an owl, not a phoenix. However, in fanfiction, the rules can be bent. Some fanfic writers might choose to make Hedwig a phoenix for creative and unique storytelling. It could add a new dimension to the story, perhaps giving Hedwig more magical abilities like the phoenix's ability to be reborn.
Hedwig can be characterized as a bit of a mischief - maker. Instead of just being a typical owl that delivers letters, she could play little pranks on Harry and his friends, like hiding their quills in hard - to - reach places.
Often, Hedwig develops a stronger bond with Harry in fanfiction. She might become more protective of him, going beyond just being his messenger. For instance, she could sense danger approaching Harry before he does and take actions to keep him safe. This shows her growth from a simple owl to a more complex character with emotions and instincts. Also, in some stories, she may develop relationships with other characters in the wizarding world, like the other owls or even some of Harry's friends, which further shapes her character.
One common theme is loyalty. Since Hedwig is Harry's owl, the fanfictions often explore how deeply loyal she is to him and vice versa. For example, in many stories, Hedwig will go to great lengths to protect Harry or deliver his messages no matter what the danger.
There is also 'Harry, Lily, and Hedwig's Adventures'. This one takes the trio on a journey through different magical realms. It's a more action - packed fanfiction where Harry discovers new things about his mother through their adventures together with Hedwig. The author does a great job of creating vivid descriptions of the magical places they visit and how Lily's presence affects Harry's growth as a wizard.
Because their relationship in the original series is so pure and deep. Hedwig is Harry's constant companion, and fanfiction writers like to explore that bond further, adding more emotional depth and different storylines.
The mental link between Harry and Hedwig in fanfiction can often be a tool for the author to create unique plotlines. Maybe Harry can communicate with Hedwig telepathically, sharing his thoughts and feelings, which Hedwig can then use to help him in some way, like warning him of danger when she's out on a flight.
It shows a very close and unique bond. Hedwig is not just a pet but a provider for Harry. By bringing dead rats, she's taking care of him in her own owl - like way, which deepens their connection.