Well, it could be that Dumbledore, in some fanfic versions, figures it out first and then reveals it to Harry. Dumbledore is often portrayed as having a deep understanding of magic. He might have noticed some strange magical patterns or behaviors related to Harry that led him to suspect and then confirm that Harry was a Horcrux. And then he would tell Harry about it, which is how Harry comes to know.
One consequence could be that Harry feels an internal struggle. Since he has a part of Voldemort's soul in him, he might have to constantly fight against the dark impulses that come with it. For example, he may find himself having more aggressive thoughts or being more easily influenced by dark magic in certain situations.
Perhaps his father's old wand. It has a connection to his family and his heritage. Since it's a wand, it already has a certain amount of magical energy, so it could potentially be a suitable vessel for a Horcrux. And it would be a very interesting twist on the concept of a Horcrux as wands are not a typical choice.
One consequence could be that his connection to Voldemort becomes even stronger. This might lead to him being able to sense Voldemort's actions and thoughts more clearly, but also make him more vulnerable to Voldemort's attacks on his mind. Since the Horcrux is a part of Voldemort's soul, it could also start to influence Harry's personality, making him more aggressive or moody at times.
Well, in some fanfictions, a Horcrux might be purified through powerful magic spells that are specifically created for the purpose. For example, a spell that can reverse the dark magic used to create the Horcrux in the first place.
If Harry were to create a Horcrux in fanfiction, it would likely lead to a great corruption of his soul. Horcruxes are dark magic, and the act goes against all that Harry stands for in the original series. He might start to show signs of increased aggression, a detachment from his friends, and a growing attraction to the Dark Arts.
It could make him more cautious. After talking to the Horcrux, he realizes how devious Voldemort's magic can be and becomes more careful in his future encounters with dark magic.
In this kind of fanfiction, it often shows Ginny's shock and the complex emotions she might have. She might be worried about Harry's fate, as being a Horcrux means he is tied to Voldemort in a very dangerous way. This discovery could lead to her trying to find a way to break the Horcrux connection without harming Harry.
It can completely change the direction of the plot. For instance, if Harry absorbs the Horcrux early on, he may have to face different challenges than in the original story. He might become a target for both sides, as the good side could be wary of his new, Horcrux - influenced state, and the bad side might see him as a threat to Voldemort's power.
The relationships between characters would also be altered. Hermione and Ron might be even more protective of Harry, but also more suspicious. They would constantly be on the lookout for any signs that the Horcrux is influencing Harry negatively. Dumbledore's plans, if he were still alive in the fanfiction, would have to be completely re - thought. The prophecy might take on a new meaning as well, since Harry now has a part of Voldemort's soul within him. All in all, it's a major plot - twisting concept.
The story would change drastically. Harry's relationships would be different. Hermione and Ron might not be able to trust him anymore. The story would likely take on a darker tone as Harry delved into the world of dark magic. Instead of being the hero fighting against Voldemort's Horcruxes, he would now be a maker of one, blurring the lines between good and evil.