The Red Skull could be the main villain. He could team up with some other super - villains or get his hands on some kryptonite - like substance. He would try to use his knowledge of Captain America's past and Superman's weakness to defeat them. He wants to rule the world and sees these two heroes as the biggest obstacles in his way.
Well, perhaps a plot where they accidentally end up in an alternate dimension. In this dimension, their powers are different. Captain America might have some super - speed and Superman might have a more tactical mind like Cap. They have to figure out how to get back to their own dimension while also dealing with the villains of this new world. They learn from each other's skills and grow closer as friends throughout this adventure.
Red Skull could be the villain. Since he has a long history with Captain America, in a fanfiction where Captain Carter is involved, he could be resurrected or have found a way to cross over from another dimension. He would see Captain Carter as an interesting new threat and Captain America as an old foe to be finally defeated.
Baron Zemo could be a great main villain. He could be plotting to create chaos between the two heroes. He might use his intelligence to set up situations where Captain America and Black Widow suspect each other, all while he is working on a larger scheme to take over a powerful weapon or organization.
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.
Lex Luthor would be a great villain. He could be plotting to destroy Superman once and for all while also trying to outsmart Batman. His intelligence and resources make him a formidable foe for both heroes.
He could also meet Odin. Odin might view Captain America as an interesting mortal from Midgard and might have some words of wisdom or a task for him to complete during his stay in Asgard.
Trigon, Raven's father, could also be the main villain. He might see Superman as a new obstacle in his path to spreading chaos and destruction. His demonic powers would be a huge challenge for both Raven, who has a complex relationship with him, and Superman, who has never faced such a dark and powerful entity from another dimension.
A fight between Captain America and Superman in fanfiction would be a complex affair. Superman has god - like powers, but Captain America has a heart of a hero. Superman might start the fight being overly confident. Captain America, though, would quickly analyze Superman's fighting style. He might notice that Superman is a bit too straightforward in his attacks. Captain America could then use his agility and shield to dodge and counter - attack. However, in the long run, without some sort of equalizer like Kryptonite, Superman's raw power would probably prevail. But the fight would be a great display of two different types of heroism, with Captain America representing the best of human courage and Superman representing the pinnacle of superhuman ability.
Often, there will be some of Captain America's old friends or comrades in these fanfics. For example, Bucky Barnes might make an appearance. He could be like an uncle figure to the son, teaching him about the old days and some combat skills. There could also be new characters created specifically for the fanfic, like a young sidekick for the son who has different powers and a different background, adding more depth and variety to the story.
Well, in this fanfic, Captain America would stand out immediately. His costume and shield would be quite the spectacle in Westeros. He might find himself in the middle of the power struggles between the Lannisters and the other houses. His leadership skills could be put to the test as he tries to unite the different factions against a common enemy, like the White Walkers, or just to bring peace to the Seven Kingdoms.