One possible plot could be that Harry accidentally breaks a valuable item on Snape's desk in the classroom. The fan could be a magical fan that Snape was using for an experiment. Snape gets angry at Harry at first but then realizes it was an accident. As they try to fix the item together, they start to understand each other better.
Maybe Harry is sent to Snape's classroom after getting into trouble. There's an old, creaky desk in the corner. The fan in the classroom is making a strange noise. Snape decides to make Harry clean the classroom as punishment. While cleaning around the desk, Harry discovers an old spell book. Snape catches him and they end up discussing the spells in the book, leading to a newfound respect between them.
One possible plot could be that Harry accidentally breaks the desk during a spell - casting practice in Snape's class. Snape then uses this as an opportunity to give Harry extra detention and during that time, they start to have a more in - depth conversation about Harry's future at Hogwarts and Snape's past with Harry's father. This could lead to a new understanding between them.
Well, the desk could be the center of attention. Maybe Harry is sitting at the desk doing a difficult potion assignment and Snape is watching him closely. The fan could be blowing some papers around, causing a distraction. Snape could then scold Harry for not focusing, but Harry could retort that the fan is the real problem. This could lead to a series of interactions between them.
I'm not sure if there is a specific fanfic that exactly meets these criteria without adult content. However, there are many fanfics about Snape and Harry that focus on their complex relationship in the Hogwarts setting. You can search on fanfic - dedicated websites like Archive of Our Own, but make sure to filter for appropriate content.
One possible plot could be that they are in the library. Hermione is looking for a particular book on the desk when Harry comes in with some newfound magical knowledge. He bends over her slightly to point out a passage in the book, leading to a moment of shared discovery and a deepening of their friendship in a platonic way.
One possible plot could be that there is a magical accident or spell that binds Harry to Snape in this 'pet - like' relationship. Snape is initially reluctant but then starts to see the potential in having Harry under his control. He could use Harry to further his own goals, whether it's to gain power within Hogwarts or to take revenge on his enemies. Meanwhile, Harry has to figure out how to reverse the situation while dealing with the new and uncomfortable dynamic between him and Snape. It would be a very different take on the Harry Potter story, full of twists and turns as Harry tries to regain his freedom and Snape tries to maintain his hold on him.
A possible plot twist could be that Snape is actually the one who arranged for Harry to be sent to Azkaban, but for a noble reason. Maybe he knew that Harry was in danger from a more powerful dark force and Azkaban was the only place that could keep him safe temporarily. Another twist could be that the real culprit behind the crime Harry is accused of is someone very close to Snape, and Snape has to choose between protecting that person and helping Harry. It could also be that Snape discovers that Harry has a hidden power while in Azkaban that could change the fate of the wizarding world, and he now has to keep Harry alive at all costs.
One possible plot development could be that Dumbledore gives Snape to Harry as a sort of guide in the wizarding world. Snape, with all his knowledge and experience, could show Harry things that Dumbledore couldn't. This might include some dark arts knowledge that could be used against Voldemort. It could also be a test for both of them. For Snape, to see if he can truly be selfless in helping Harry, and for Harry, to learn to trust Snape despite their past differences.
One possibility is that this is a misnomer or a very tongue - in - cheek title. In the fanfiction, it could be that Harry is using some new form of magic under Snape's desk that has an effect that can be humorously described as'sucking'. For instance, he could be using a spell to draw out negative magical energy that has accumulated under Snape's desk, which is causing problems in the classroom, and the spell's action makes it seem like he's'sucking' something out.
Well, it could be about Harry finding a hidden magical object under Snape's desk. Maybe it's a potion ingredient that Snape has been secretly guarding. Harry, being curious, decides to investigate further and gets into all sorts of trouble as a result.
One possible plot idea could be how Snape deals with the physical and emotional changes during the pregnancy while still trying to maintain his role at Hogwarts. Another could be the reactions of other characters like Harry, Hermione, and Ron when they find out.