One great fanfiction could be 'A Bond Beyond War'. It beautifully depicts the relationship between female Byleth and Dimitri as they navigate the challenges of war and politics together. Their interactions are filled with a mix of loyalty, friendship and a budding romance.
Another theme is leadership. Edelgard as an emperor - to - be and Byleth as a teacher - turned - ally often have to lead together. They face the challenges of ruling and guiding their people, like in the fanfic 'Guiding Fódlan'.
The theme of growth is also prevalent. Both characters grow as individuals and as a couple (if it's a romantic story). The female Byleth might grow in her understanding of the world around her, while Dimitri grows in his leadership skills and emotional stability, all while their relationship develops and deepens over the course of the story.
In a fanfiction, Dimitri and Female Byleth could have a story where they are forced to make difficult decisions. Maybe they are at odds with their own kingdoms' politics at some point. Byleth, with her connection to the divine, might guide Dimitri in seeing a different perspective. They could have a love - hate relationship initially, with Dimitri's pride and Byleth's no - nonsense attitude causing friction, but over time, they come to understand each other better and form a strong alliance.
Often, her strong leadership is depicted. In many fanfictions, female Byleth is shown leading her students or allies into battle with confidence. Her kindness towards the students is also a common characteristic. For example, she might comfort a troubled student. Another is her determination. Fanfictions may show her facing difficult challenges and not giving up, like when she has to make tough decisions in the story.
They could have a story where Dimitri is in need of redemption and Byleth is the one to help him. Byleth's presence could be like a light in Dimitri's dark world. She could use her teaching skills to help him regain his sense of self. Their relationship could be one of teacher - student turned into something more romantic as Dimitri heals and grows under Byleth's influence.
One great female Byleth fanfiction is 'The Professor's Path'. It delves into her journey as a teacher in the academy, exploring her relationships with the students in a very heartwarming way. Another is 'Byleth's Ascent' which focuses on her growth in combat skills and how she overcomes various challenges in battles. And 'A Day in the Life of Female Byleth' gives a detailed look at her daily routine, from training sessions to interactions with other characters.
A common theme is the power dynamic between them. Given Edelgard's position as an emperor and Byleth's role as a teacher and later an important figure in Edelgard's life. Another theme is trust - building. Since they come from different backgrounds and have different goals initially, seeing how they come to trust each other is often explored. Also, there's the theme of love in the face of conflict. Their relationship is often set against the backdrop of the political and military turmoil in the game's world.
In 'Fire Emblem Female Byleth' fanfiction, a major theme is her role in the overall story. Is she a hero, a guide, or something else? Another common theme is her emotional journey. She has to deal with loss, love, and hope. Also, the fanfictions often explore her connection to the Fire Emblem itself. How does it affect her powers and her destiny? And her interactions with different factions within the game world also make for a common theme, as she has to navigate political and social situations.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). There are often tags for Fire Emblem and specifically for Byleth and Edelgard. Just search for their names and you'll find a variety of stories. Another option is FanFiction.net, though the selection might be a bit different.