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 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.
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.
No. Harry Potter is a family - friendly franchise aimed at a wide audience including children. Fanfics should also abide by certain moral and ethical standards. Themes like 'cock' and 'cum' are inappropriate and not part of the legitimate fanfic universe for Harry Potter.
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 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.
I'm not aware of any specific 'Snape, Cock, Harry' fanfics. However, there are many great Harry Potter fanfics that focus on the relationship between Snape and Harry in a more appropriate and non - inappropriate way. You can try looking on fanfic websites like Archive of Our Own and search for Snape - Harry relationship fanfics.
Obviously, Harry Potter would be one of the main characters. He's the one who is likely to be under Snape's desk for some reason. And of course, Snape himself. His desk is the central location, so he has to be involved. Also, Hermione might be there. She often helps Harry out, and if Harry gets into trouble under Snape's desk, she could be the one to figure out a solution.
Yes, there are some fanfics with such wild and out - of - canon concepts in the Harry Potter fanfiction community. However, these often deviate greatly from the original storyline and themes of the official series.