One great 'Fem Harry Abandoned by Parents' fanfiction is 'A Different Beginning'. It explores how a female Harry copes with being left alone at a young age. The story delves deep into her emotions and her journey to find her place in the wizarding world. The character development is really well - done, and it's a captivating read.
One interesting fanfic could be where Harry is abandoned as a baby but is found by a group of magical creatures who raise him. They teach him unique magic that Hogwarts doesn't offer. Another might be a story where Harry is abandoned and ends up in a different magical realm altogether, having to find his way back to the wizarding world while uncovering secrets about his parents.
A third plotline might be that Harry is abandoned in a magical but hidden place. There, he is raised by magical creatures, say, a group of centaurs. They teach him their own brand of magic and wisdom. When he finally enters the wizarding world proper, he has a very different perspective on magic compared to the other students, which causes both admiration and some envy among his peers.
One possible plotline could be Harry growing up in an orphanage where he discovers some latent magic powers on his own before getting his Hogwarts letter. He might face more difficulties and prejudices from the muggles around him, which could make his entry into the wizarding world even more of a relief.
The search for identity is a prevalent theme. Being abandoned by her parents makes Fem Harry question her heritage and her place in the wizarding world. She might explore her mother's or father's side in different ways. Some fanfictions also have a theme of revenge, where Fem Harry wants to get back at those who caused her parents to abandon her, but this is less common compared to the others.
One great fanfiction could be 'The Orphaned Wizard's Journey'. It delves deep into Harry's emotions as he copes with the abandonment. Another is 'Abandoned but Not Alone' which focuses on how he finds a new family in his friends at Hogwarts. And 'Harry's Solitary Struggle' shows his inner strength as he faces the world without his parents.
It shows his vulnerability. Without his parents, Harry is in a very fragile state at first. He has to learn to deal with loneliness and the feeling of being unwanted.
He might be more distrustful. The feeling of being abandoned could make it hard for him to trust others easily. For example, when he first meets Dumbledore or his new friends at Hogwarts, he may be hesitant to open up completely because he's been let down by the most important people in his life - his parents.
Often, it changes the power dynamics. Instead of growing up with the Dursleys, Harry might grow up in a completely different environment, which gives him different skills and knowledge. For example, if he's raised by magical creatures, he could have a deeper understanding of nature magic.
He might turn to his studies more intensively. Since he has no friends to distract him, he could pour all his energy into learning new spells and magic, becoming more powerful in the process.