One interesting story could be about Batman being tempted by the power of the Yellow Lantern ring. Maybe he struggles with the fear - based power it offers while still trying to uphold his own code in Gotham. For example, he might face off against his rogues gallery in a new way, using the yellow energy but also fighting not to be fully consumed by it.
Batman and the Yellow Lantern could start off as enemies. Batman is all about justice and the Yellow Lantern's power is based on fear, which goes against Batman's principles. So there could be a lot of tense confrontations at first.
The Black Lantern origin story has deep roots in the DC Comics mythology. It begins with Nekron, a being of death. Nekron creates the Black Lantern power rings. These rings have the ability to seek out the dead across the universe. The rings are attracted to those with strong emotions, particularly negative ones like fear and anger. Once a dead body is chosen by a black ring, it is reanimated into a Black Lantern. The Black Lanterns are not like normal undead; they have a unique power source related to death energy. They can also use the emotional energy of fear from living beings to fuel their powers. This makes them a very dangerous and terrifying force in the DC Comics universe, often causing chaos and destruction as they carry out Nekron's dark plans.
There are fanfictions where a Yellow Lantern OC teams up with an unlikely ally from a different Lantern Corps. For example, an OC Yellow Lantern and a Green Lantern might have to work together to stop a greater threat, which makes for an interesting dynamic as they have such different outlooks based on their Corps.
Well, obviously Batman himself is the main character. He's the one who gets caught up in the Yellow Lantern concept. Then there are often the Yellow Lantern Corps members. Characters like Sinestro might make an appearance as he is a major figure in the Yellow Lantern Corps. They would be the ones trying to influence Batman or fight against him depending on the plot.