It could be that the pet is magically attracted to the glasses. Maybe the glasses have a certain charm or power that the pet senses, and it tries to steal them to bring back to Voldemort. For example, if the glasses can see through certain dark magic disguises, Voldemort would want to get his hands on them through his pet.
The pet could try to break Harry's glasses. Since Voldemort hates Harry, his pet might be programmed or trained to destroy things that are important to Harry. The glasses are a very visible and important part of Harry.
In some fanfictions, Voldemort's pet might be used as a symbol of his power and evil. Harry's glasses, on the other hand, are an iconic part of his character. The combination could be used to create a unique plot. For example, Voldemort's pet might steal Harry's glasses to disrupt his vision and thus his ability to fight. It could also be a more symbolic connection, like the pet representing Voldemort's hold over Harry's life, and the glasses being a symbol of Harry's identity that Voldemort wants to break.
The pet could act as a catalyst for certain events. Say it's a creature that can manipulate time in a small way. It might accidentally or purposefully change some key moments in the story, like preventing Harry from getting a certain magical item that he needs to defeat Voldemort.
One possible plotline could be that Voldemort's pet somehow steals Harry's glasses as a way to taunt him. This could lead to Harry going on a quest to retrieve them, facing various dark magic obstacles along the way.
The fanfiction could explore a scenario where Harry's glasses are taken away as a way to break his spirit. Voldemort, having Harry as his pet, might want to completely subdue him. Without his glasses, Harry has to navigate a blurry world. This could lead to some interesting interactions with other characters. For example, Hermione might try to find a magical way to restore Harry's vision or at least give him some form of sight assistance without glasses. Ron, on the other hand, could be conflicted about whether to help Harry escape Voldemort's clutches or if he should follow Voldemort's orders as well since Harry seems so different without his glasses.
Some fanfictions may depict that Harry's children are transported to a parallel dimension where Voldemort never died. Here, they have to directly interact with Voldemort in his full power. They might try to use their own unique magic, inherited from Harry and their mother, to outwit Voldemort and find a way to return to their own dimension, all while avoiding being killed by Voldemort and his Death Eaters.
The pet could be a key factor in changing Harry's perspective. If it's a friendly and wise pet, it might give Harry new insights into Voldemort's motives, making Harry more determined to end him. For instance, if the pet was a magical cat that could communicate with Harry telepathically, it could share some deep secrets about Voldemort's past that fuel Harry's fight.
In some Harry Potter fanfictions, Voldemort's pet could be a large and menacing snake, like Nagini. Since snakes are often associated with Slytherin and Voldemort was a descendant of Slytherin, it makes sense for his pet to be a snake. It could also be some sort of dark magical creature, perhaps a basilisk under his control. Another possibility is a magical raven or crow, which could be used as spies for him, flying around Hogwarts and other places to gather information.
No. In the original 'Harry Potter' series, Harry is Voldemort's archenemy, not his pet snake. Fanfiction might play with strange and unorthodox ideas, but this goes against the fundamental nature of their relationship in the official story.
Voldemort's daughter herself would be in a very difficult position. She might be shunned by many in the wizarding world just because of who her father is. But some might be curious about her. For example, Luna Lovegood could be one of the first to approach her without judgment, which could start a chain reaction of other characters slowly warming up to her. And the Death Eaters might try to manipulate her into following in her father's footsteps.