Perhaps Peter's job in the bar is a way for him to gather information. He might be on a secret mission, and the bar is a place where all kinds of characters come. He has to blend in as a bartender while listening for any useful news. He could meet old Narnian friends or foes in disguise there.
Peter might encounter a mysterious customer who knows his true identity from Narnia. This could lead to either danger or an opportunity for him. For example, the customer could offer him a way back to Narnia.
One idea could be a story where Peter and Caspian have to go on a secret mission together to find a lost magical artifact that can save Narnia from a new threat. They start off not getting along but gradually learn to respect each other's skills.
Maybe Peter meets some interesting characters at the bar. It could be an old scientist who gives him some insights on new web - shooting technology. This could help him improve his Spider - Man gear. Also, the bar could be a place where he unwinds after a long day of fighting crime, and he might meet a girl there who is initially attracted to the normal 'Peter' not knowing he's Spider - Man.
There's also 'Lucy's Secret Journeys'. In this fanfiction, Lucy discovers a hidden power within herself and Peter has to help her control it. It's full of emotional moments and great character development. The author does a wonderful job of staying true to the original characters while adding new twists.
Another job Peter might have in fanfiction is working at Oscorp. This is a very interesting take as it puts him right in the middle of the action with all the scientific research and potential villainous plots going on there. It can lead to many exciting storylines where he has to balance his job duties with his secret identity and the need to stop any evil plans brewing at Oscorp.
The theme of redemption can also be found. Sometimes an original character has made mistakes in the past and through their interactions with Peter, they seek redemption. Additionally, the theme of family is there. Even though the original characters are new, they often become part of Peter's 'family' in Narnia, and they learn the importance of family bonds and loyalty.
Websites like Archive of Our Own (AO3) are great places to start. It has a large collection of fanfiction, and you can easily search for 'Harry Potter' and 'Peter Pevensie' crossovers. There are filters to help you find the most popular or recently updated ones.
One great 'Harry Potter' and 'Peter Pevensie' fanfiction is 'The Unlikely Alliance'. It combines the magic of Hogwarts with the Narnian world in a really interesting way. The characters from both universes interact in a believable manner, like Harry and Peter teaming up to fight a common enemy that threatens both their worlds.
You can start by looking on fanfiction.net. It has a large collection of fanfictions, including many about Peter and Lucy Pevensie. Just search for their names in the search bar.
There might be a fanfiction where Peter Pevensie attends a magical school similar to Hogwarts but with Narnian elements. He could befriend students from different magical realms and they all go on quests together within the school grounds. It would be a great blend of the Narnia universe and the concept of a school - based magical adventure.