One common theme is family. Since there's a baby involved, it often explores how Amy, Shadow, and the baby form a family unit. Another theme could be protection. They usually have to protect the baby from various threats.
A great 'amy rose and shadow baby fanfic' that I've come across is 'The Bond of Amy, Shadow, and Their Baby'. This one really emphasizes the emotional bond between the characters. It starts with Amy and Shadow unexpectedly finding themselves responsible for a baby. As the story progresses, they learn about love, sacrifice, and the true meaning of family. The way the author portrays their struggles and joys makes it a very engaging read.
You can try fanfiction.net. It has a large collection of fanfics from various fandoms, and there's a good chance you'll find some amy rose shadow fanfic there.
One good amy rose shadow fanfic could be 'The Adventures of Amy and Shadow'. It might involve their adventures in a magical world where they team up to defeat an evil force. In this fanfic, their unique personalities would shine through as they face various challenges together.
There might be a 'amy rose baby fanfic' where she teams up with her friends to raise a baby that has special abilities. They have to figure out how to help the baby control its powers while also dealing with daily life challenges.
The relationship would likely deepen with more shared responsibilities. They might argue at times over different ways of bringing up the baby, but these arguments would also strengthen their bond as they learn to understand each other's perspectives better. There would be more tender moments between them as they watch their baby grow, and they would be more united against any threats to their family.
Amy Rose has a deep affection for Sonic, not Shadow. So in the official Sonic lore, there is no such love story between Amy Rose and Shadow. However, if we were to imagine it, perhaps they could meet during a fight against a common enemy. Shadow, initially cold and distant, might be gradually warmed by Amy's persistent kindness and her strong will. And Amy might be attracted to Shadow's mysterious and powerful nature.
Even one of her friends like Tails could be the betrayer in a really unexpected plot twist. Maybe Tails is forced to betray her by some external threat. For example, if an enemy captures Tails and threatens to harm him or Sonic if he doesn't give away some important information about Amy Rose or lead her into a trap.
A 'amy rose dies fanfic' could be a very sad and dark take on the character. It might explore themes like loss, grief among the other characters who knew Amy Rose. Maybe it's a way for the writer to show how her death could impact the whole story's universe.