Captain America's fate in the comics is a bit convoluted. Different story arcs and villains play roles in his supposed 'death', but it's not straightforward to pin it on one individual.
In the world of fanfiction, the idea of Iron Man killing Captain America can be quite controversial. Ethically, it goes against the typical heroic and friendly relationship they have in the mainstream Marvel universe. However, fanfiction is a space for exploring different scenarios, so while it may seem unethical to some, it can be a creative exploration for others.
I'm not aware of any official 'Captain America Kills Spiderman' fanfic. This concept goes against the general heroic and friendly relationship between the two characters in the Marvel universe. However, in the realm of fan - created works, anything can be imagined, but it would be a very dark and out - of - character take.
One possible reason could be mind control. Maybe an enemy has the ability to control Captain America's mind and make him turn on Spiderman. Another reason might be a misunderstanding. For example, if Spiderman was framed for a crime he didn't commit and Captain America believed the false evidence.
One possible plot reason could be a major ideological difference that escalates out of control. For example, they might have a huge disagreement over the use of a new technology or how to deal with a particular threat, and Iron Man in a fit of rage or desperation takes it too far and kills Captain America.
There's also the story of Steve's first real mission as Captain America. He was sent on a USO tour at first, but when he got the chance to fight in the real battle, he showed his true courage. He didn't care about the danger and just wanted to do his part to save his comrades and fight against the bad guys.
Well, in some fanfics, they might make Captain America seem like a jerk to create an interesting plot twist. Maybe they show him being overly self - righteous or making bad decisions that go against his usual heroic image.
One idea could be a story where Captain America and Captain Marvel team up to face a new cosmic threat that's headed towards Earth. They have to combine their unique skills, with Captain America's strategic mind and combat experience on the ground, and Captain Marvel's incredible cosmic powers in space battles.
The Night King could be a great antagonist. His army of the dead and his own powerful magic would pose a huge threat to Captain America. Cap's used to fighting human foes, but the Night King is something entirely different.