There are fanfictions where Snape aids Harry in understanding some of the more complex aspects of the wizarding world, like the history of certain dark families or the origin of some dark spells. This is because Snape has a deep understanding of both the light and dark sides of magic. Also, during times of war in the fanfiction world, Snape might share some strategic information with Harry to help him fight against Voldemort and his followers.
One common scenario is Snape helping Harry with his Potions work. Since Snape is the Potions master, he might offer some extra guidance to Harry, which could be crucial for Harry's progress in school. Another scenario could be Snape protecting Harry from the bullying of other Slytherins. He might not do it in an obvious way, but still intervenes subtly.
One common scenario is during the Triwizard Tournament. Maybe Fleur is struggling with a task, like the second task in the lake. Harry, having already completed it, could give her some tips on how to find the hostages or deal with the merpeople. Another scenario could be when Fleur is facing some form of discrimination or bullying at Hogwarts or in the wizarding world. Harry, being a champion of justice, would step in to support her.
One common scenario is when Harry is in trouble at Hogwarts. Sirius might break into the school in his animagus form to rescue Harry. Another is when Harry is dealing with the mystery of his parents' death. Sirius can share memories or information that he has about that time, like what really happened the night they died. He can also help Harry deal with the Dementors, as he has his own experiences with them.
One scenario could be that Harry uses his invisibility cloak to help Crane study his patients without being noticed. This would allow Crane to get a more accurate understanding of their behaviors.
A good place to find Snape - helps - Harry - Potter fanfictions is Fanfiction.net. It has a large collection of Harry Potter fanfictions, and you can use the search function to look for stories specifically about Snape helping Harry. Just type in relevant keywords like 'Snape helps Harry' and you'll get a list of stories.
Often, in the fanfic, it could be that Harry is injured during a Quidditch match. Snape, despite his dislike for Harry in some ways, realizes the importance of Harry to the wizarding world and heals him. There could also be a situation where Harry is affected by some dark magic in the Forbidden Forest. Snape, who has a deep understanding of dark magic, is the only one who can counter it and heal Harry. It might also happen that Harry is suffering from the after - effects of using powerful magic, and Snape uses his own unique magic to heal Harry's drained energy.
One common scenario is after a battle. Harry is injured, and Snape, despite their differences, steps in to heal him. Maybe it's a fight against the Death Eaters where Harry is seriously wounded, and Snape realizes he has to put aside their enmity for the greater good.
One scenario could be that Snape holds Harry Potter captive to protect him from a greater threat that he's aware of but Harry isn't. Maybe he has learned of a new dark wizard's plot against Harry and by holding him, he can keep him in a magically protected area until the danger passes.
One great fanfiction where Snape helps Harry Potter is 'The Unseen Bond'. In this story, Snape secretly protects Harry from a new dark threat at Hogwarts. He uses his knowledge of the Dark Arts to counter the enemy's spells. This shows a different side of Snape, one that is more benevolent towards Harry.
A common scenario is that Harry is made to scrub cauldrons. Snape would be hovering nearby, making sarcastic remarks about Harry's sloppiness. Another one could be that Harry has to organize Snape's Potions ingredients in alphabetical order while Snape quizzes him on their properties.
One common scenario could be that Harry is caught sneaking around the Slytherin common room or stealing potions ingredients from Snape's stores. So, Snape and Draco might make him do extra detention tasks like scrubbing the cauldrons for hours without magic. Another situation could be if Harry is suspected of cheating in a Potions exam. Draco might report it to Snape, and they could punish Harry by making him redo all his Potions experiments from the semester.