This should be the easy part, right? You and your readership are already familiar with this individual.
Another author has already envisaged how they look, act, speak, think and react in certain situations. You know their stories and what they like to eat and drink. You have their idiosyncrasies and traits already laid bare. Their favorite music, hobbies and fashions are there for the plundering. You can deduce the sort of people they love, hate and who becomes their friends.
You know all of that, but so do your readers. Fandoms form around personalities (fictitious or otherwise) with whom enough people identify. They are all seeing something here, which chimes with something inside themselves.
To spell this out: whatever you write about their favorite canon character could easily be framed as a commentary upon themselves. Tempers could get frayed accordingly.
Moreover, everyone's an expert. Each one of your readers will secretly believe that he or she is this canon's number one fan. If you interpret the character in a vastly different way, then you should be prepared to defend it with endless reference to the original source.
If you can't, then the next accusation will be one of having written out of character (OOC). If you're doing that, then you're not writing fan fiction. It's an original story with stolen names. That's false advertising again!
There are only three ways to avoid that:
The first is to simply rewrite the canon without changing much at all. Not only is that boring, but you've immediately placed yourself in a side by side comparison with the original. That's the one with the fandom and the sales. Good luck there. Shakespeare pulled it off with Romeo and Juliet, so there is hope.
The second is to openly state, in the author's notes or introduction, that you're being experimental. It will be OOC, but you wanted to see what would happen if some details were different. If your pride can stand it, then this will head off any criticism and render fans more open to your interpretation.
The third will demonstrate precisely why rewriting canon characters is not the easy part. It involves sitting for hours, days or weeks scrutinizing every bit of every scene and taking notes. You need to justify every fact, every inclusion, every whim of characterization.
Not only will this result in a person on your page which should be recognizable, but it will be your defense against OOC characterization. Actually become the expert that everyone thinks that they are; and be ready with chapter and verse to refute all comers in the comments.
Recreating canon characters is like walking in somebody else's footsteps across a snowy field. Everyone can see precisely where you should step, and will know instantly if you're out by just an inch. Why on Earth would anyone assume that's easier than simply forging your own path to the other side?