Yes, there are likely some out there. You can start by checking fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'hell kaiser watches syrus' in the Yugioh section and you might find some interesting stories.
A plot could involve Hell Kaiser being sent to evaluate Syrus for some special training program. As he watches Syrus, he discovers that Syrus has some unique qualities that could be both an advantage and a disadvantage. There could be a conflict where Hell Kaiser has to decide whether to report accurately or help Syrus overcome his weaknesses first. The story could also include duels where Syrus shows his growth under Hell Kaiser's watchful eye.
One likely antagonist could be Chazz Princeton. He's often shown as a bit of a bully in the Yugioh series, and he might target Syrus out of jealousy or just to assert his dominance. Another could be an original character created by the fanfiction writer, perhaps a new student at Duel Academy who has a vendetta against Syrus for some reason. The Society of Light could also be antagonists in a sense, as they might try to manipulate Syrus or use him in their schemes, which could lead to him getting hurt.
One common plotline could be Syrus facing bullying at Duel Academy which causes him emotional hurt. Maybe some upperclassmen pick on him for his dueling skills or his timid nature. Another could be Syrus getting hurt in a dangerous duel, like against a powerful opponent who uses underhanded tactics. Also, he might get his heart broken in a romantic sub - plot within the Yugioh world, perhaps by someone he has a crush on who doesn't return his feelings.
One possible plot could be that Syrus, while exploring an ancient library in the Duel Academy, stumbles upon a hidden spellbook that has a connection to the Dark Magician Girl. He accidentally summons her in a weakened state. Then, they have to work together to regain her full power while facing various challenges from other duelists who want to capture the Dark Magician Girl for their own purposes.
Their interaction could start with Syrus having a strange dream about the Dark Magician Girl. When he wakes up, he starts noticing little signs around the Duel Academy that seem to be related to her. One day, while dueling, he makes a move that somehow creates a small rift in the magic world, and the Dark Magician Girl steps through it for a brief moment. That moment of eye contact is the start of their interaction.
The Baby Dragon could be a symbol of hope in a dark world created by the Hell Kaiser in a fanfiction. The dragon's purity and power could start to influence the Hell Kaiser, slowly changing his perspective. As they interact more, the Hell Kaiser may find himself drawn to the dragon's positive energy, and this could lead to a complete transformation of his character over time.
There could be a story where the Hell Kaiser, known for his cold and calculating style, is unexpectedly moved by the innocence and potential of the Baby Dragon. This causes a change in his dueling philosophy. He may start to question his cut - throat ways and consider a more balanced approach to dueling, all because of his encounter with the Baby Dragon in the fanfiction world.
It's quite normal. In a fandom, people are interested in different aspects of the characters. Zane might be curious about Syrus's backstory, relationships, or potential storylines that fanfiction writers have created. It's just another way of engaging with the fictional world they are part of.
Another aspect of their brotherly love in fanfiction could be the way they support each other during tough times. Syrus might be having a hard time with his self - confidence, and Zane would be there to encourage him. He could tell Syrus about his own insecurities when he was younger and how he overcame them, thus inspiring Syrus to grow and believe in himself more.