You can start by looking on some of the major fanfic websites like Fanfiction.net or Archive of Our Own. Use the search function and type in 'Harry Potter' along with 'abandoned' to filter out the relevant stories.
A magical creature native to China could be a main character. Maybe a phoenix - like being but with unique Chinese characteristics. It could communicate with Harry Potter in some way and help him on his journey. It could have powers that are different from the magical creatures Harry is used to in the UK, and they could form an unlikely bond as they face the mysteries together.
Perhaps Harry Potter gets lost in a mysterious Chinese magical forest. In this forest, he encounters ancient Chinese magic that is both fascinating and dangerous. He has to use his existing skills from Hogwarts along with what he learns in this new environment to find his way out and also figure out why he was abandoned in China in the first place.
There are some 'Harry Potter' abandoned fanfics that deal with different magical creatures in more depth. For example, fanfics that show how the centaurs' society works in great detail or how the merpeople communicate. These can be really fascinating as they expand on the magical world created by J.K. Rowling. However, since they are abandoned, they might end on cliffhangers.
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.
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.
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.
Well, just based on that title alone, it's difficult to determine its quality. There are so many aspects that make a Harry Potter fanfic great. For example, it could explore new relationships between the characters, or create exciting new magical adventures. But we don't know if 'skull is harry potter fanfic' does any of those things. So, it might be good, it might not.
The theme of heartbreak is prevalent. Hermione is usually deeply hurt by Harry's abandonment, and this heartbreak can lead to different paths for her character. Also, the theme of redemption for Harry. In many of these fics, Harry realizes his mistake and tries to make amends. Sometimes it's a long and difficult journey for him to earn Hermione's forgiveness.
Some potential new allies could be the house - elves. They might see Harry's plight and decide to help him, using their unique magic and knowledge of Hogwarts' secrets. Another could be the centaurs in the Forbidden Forest. They are very wise and may take Harry under their wing.