The story could develop in many ways. For one, Izuku might resist All For One's influence and try to escape on his own. He has a strong sense of justice and would not be easily swayed.
If All For One kidnaps Izuku in fanfiction, Izuku's friends would surely try to rescue him. They could form a plan, with Bakugo being especially determined as he has a long - standing relationship with Izuku. All Might might also get involved, using his remaining power to try and save his successor.
In some fanfictions, Aizawa might be under the influence of a villain's quirk that makes him act against his will. So, he kidnaps Izuku, but later on, he realizes what he's done and tries to make amends. This could lead to a story full of drama and redemption.
It could be Aizawa himself if he's being controlled by something or has some sort of ulterior motive that is not in Izuku's best interest. But if not Aizawa, then there could be a hidden villain who is manipulating Aizawa to kidnap Izuku.
You can try websites like Archive of Our Own (AO3). It has a large collection of fanfiction for various fandoms, including My Hero Academia where Izuku and these powers are from. Just use the search function and type in relevant keywords like 'Izuku' 'All for One' 'One for All' to find the fanfictions you're interested in.
One interesting fanfiction could be where Izuku uses the combination of All for One and One for All in unique ways to defeat powerful villains. He might use All for One to take away the quirks of enemies and then use One for All to enhance his physical abilities to an even greater extent than normal.
Izuku's character would likely be very different. He might be more cynical at first. Since he's raised by All for One, he would be exposed to a lot of villainous thinking. But as he grows, his inborn sense of justice could start to resurface and cause internal conflict.
One interesting izuku all for one fanfiction could be where Izuku uses the All for One power in unexpected ways to save his friends. For example, he might use it to transfer quirks temporarily to those in need during a battle, creating unique and exciting fight scenes.
Obviously, Izuku is the main character. He's the one who is mastering One For All. All Might also often appears as he was the previous user and is Izuku's mentor in many fanfictions. Bakugo can also be a significant character as he serves as both a rival and sometimes an unexpected ally to Izuku in his journey with One For All.
One interesting story could be about Izuku exploring new powers of One For All in a different dimension. He might face challenges that test his limits and how he uses the power in unique ways.