Batman could also appeal to Jason's sense of self - improvement. He might tell Jason that quitting smoking is a step towards becoming a better version of himself, more disciplined and in control. By giving up this bad habit, he can focus more on his crime - fighting and self - development. He could also use his own example of a healthy lifestyle to inspire Jason.
I really like 'Jason Todd's Return: Arkham Knight's Hidden Story'. This fanfic focuses on Jason's role in the Arkham Knight events from a different perspective. It shows how he might have been feeling during all the chaos, and it gives a more sympathetic view of his actions. It's a shorter read but still packs a punch in terms of character exploration.
Well, in this fanfic, perhaps the Justice League has been poisoned or mind - controlled. Batman, being the resourceful hero he is, might first analyze the situation carefully. He could then track down the source of the problem, whether it's a new super - villain or an old enemy with a new trick. He'd likely use his Bat - computer to find a cure or counter - measure and then fight his way through any minions to administer it to the League members, saving them from certain doom.
It could be Lex Luthor. He's always been a big threat to the Justice League and would be a likely choice as the main antagonist in a story where Batman has to save the League.
One key event might be the initial confrontation. Batman discovers that Jason smokes and decides it's something that needs to stop. He then sits Jason down and has a serious talk with him about the dangers of smoking.
Jason could show care for Batman in fanfiction by having deep, heartfelt conversations with him, revealing a hidden soft side. He might also take on dangerous tasks alone to spare Batman from harm or work behind the scenes to gather crucial information that benefits Batman's endeavors.
He could be portrayed as having a glimmer of humanity left. His actions of saving someone would show that there is more to him than just being a mindless killer. Maybe there's some internal struggle within him as he goes against his usual nature.
Their relationship would become more complex. Batman might start to see the Joker in a different light, perhaps as a victim of his own madness rather than just a pure villain. The Joker, on the other hand, might be confused by Batman's act of saving him and could develop a strange respect for Batman, or he might try to use it to his advantage in some new, devious plan.