In the fanfiction, perhaps there's a new recruit in the Joker's gang who is very talented and starts getting a lot of attention. The Joker, being used to being the center of attention, gets jealous. He might start giving the new recruit impossible tasks to do in order to undermine them and regain the spotlight.
Another situation could be when the Joker's partner is praised by the citizens of Gotham. The Joker hates when others get any form of positive attention that he thinks should be his. So, he might plot some elaborate scheme to make his partner look bad in the public eye just to satisfy his jealous nature.
A common scenario is when there's a new character introduced. This new person starts getting a lot of attention from Blake's significant other or close friends. For instance, if Blake has a romantic partner, and a new person joins their group who is very charming and friendly, Blake might start to feel jealous as she sees her partner enjoying the new person's company.
One common scenario is when a new character is introduced. If this new character shows an interest in Starfire, Robin gets all riled up. He starts doubting himself and thinking that Starfire might like this new person more.
A common scenario is when Naruto is given a special mission or task that Sasuke feels he should have been chosen for. Sasuke's pride and his competitive nature with Naruto make him jealous. He might think that Naruto is being favored over him.
A common scenario is when Naruto is praised by someone else, like another ninja in the village. Sasuke may get jealous because he wants to be the one Naruto looks up to or the one whose opinion matters most to Naruto. Another scenario could be when Naruto makes a new friend, and Sasuke sees them spending a lot of time together. He might feel left out and jealous.
One common scenario could be when another guy shows interest in Sailor Moon. Darien might see this guy being overly friendly or flirting with her at a party or in public. For example, if a new hero from another planet arrives and is immediately drawn to Sailor Moon's beauty and power. Darien would start to feel jealous, his eyes narrowing as he watches them interact. He might become more possessive, trying to keep Sailor Moon closer to him and away from the new guy.
One common scenario is when another girl shows interest in Percy. For example, if a new demigod arrives at Camp Half - Blood and she's constantly around Percy, Annabeth might get jealous. She could start acting cold towards Percy or be overly critical of the new girl. Another situation could be if Percy has to go on a quest with a female partner and they seem to be getting along really well. Annabeth might worry that Percy will develop feelings for this other girl.
One common scenario is when Koga gives Kagome a gift. Inuyasha will feel jealous and might try to find a better gift for Kagome. Another scenario is when Koga saves Kagome from danger. Inuyasha will be jealous that Koga got to be the hero instead of him. He'll then vow to protect Kagome better in the future.
A common scenario is when Sly is teamed up with a new female thief. Carmelita would see them working closely together and get jealous.
The Joker himself is obviously the main character when it comes to his jealousy. Harley Quinn is often involved as she has a complex relationship with the Joker. Batman can also be part of the story in some cases. For example, if Batman is seen as a rival for Harley's attention in a strange way, the Joker might get jealous. Even though Batman is his enemy, the idea of Harley being interested in Batman in any way could trigger the Joker's jealousy.
One possible scenario is when the Black Cat and the male character MJ is interested in, say Spider - Man, have a secret mission together. MJ might find out about it and feel left out, leading to jealousy. Another scenario could be if the Black Cat flirts openly with the character and he seems to enjoy it. MJ would then feel jealous as she might think she's losing his attention.