From one writer to another don't do it. Don't fucking do it. Don't even entertain the thought of doing it, no matter how much people clamour for it. Writing for other people's characters is HARD, and I had the advantage of being able to talk to the author(s) of the characters I've written for on a daily basis. You will start off, as every writer before you has (you didn't think you were the first, did you? Literally tens of people have tried this and failed) with good intentions. As time goes on you will begin to wonder if your writing is up to par with theirs, but more importantly also whether you're even writing in the same style. Here's the most difficult part of writing on someone else's behalf - it's really, really hard to know exactly what was intended for the character, or how they would react in a situation, and without the ability to even contact the original author your only option left is to take it entirely into your own hands and write the character how you think it should work, which is nerve-wracking. More important than the quality of the writing is the reasoning of the writing - are you hitting the same notes? The original reason people enjoyed this character, are you continuing along those lines? Can you say, with certainty, that you even know the reason people enjoy the character? Perhaps people don't like them for the same reason you do.
I say this not because I think you're not good or smart enough or some other bullshit but because you are a nice, promising writer and I don't want you - like many others - to flame out while writing someone else's stuff. I'm 99% sure Couch covered this in the past at some point saying basically what I am, and he was right. It was a bad idea then and it's a bad idea now. Keep writing cool stuff, but it's best to let sleeping dogs lie. I know this comes off strong but I want to make it really clear that you (and every other potential writer) deserve better than burning out on something like this.