I have a strange question that I just feel the need to ask, how do you classify God in a fan fiction?

I would just use the word God.

I don't see why you can't use it.

I think there's a bit of confusion in your explanation about fiction/non-fiction, OC or not. Fictions are works coming out of someone's imagination (novels fall into that category), while non-fiction are all the works that do not tell an imaginary story but rather deals with concepts (political essays, for example) or with the true story of someone famous (a biography). Whether you believe in God has nothing to do here. It's like science-fiction or heroic fantasy : whether we believe in it or not has nothing to do with it : they are fictional works. Look at Harry Potter : these books are fictional works, whether we believe in magic or not.

In FF.net, the characters that belong to the series/movies/books/etc are listed. If any character you create or make appear in your story is not part of the "cast" of characters of the series/movies/books/etc, then it falls into the category of "original character". Hence if God is not a character from the original series/movies/books/etc, if God is in your story because YOU wanted Him to be there, so He is an "original character". It has nothing to do with believing in God or not.

As for your use of GOD as a word in your story, be aware of this : we are limited in words to grasp concepts far above our limited understanding. God is a reality that no word on this earthly plane can grasp, hence our imperfect words to call him. Hence His many names. We use GOD as a practical way to name the concept of Deity. The same goes for the use of the male pronouns to address God : He, Him, His, etc. (with a capital, to show we're talking about God). This is purely a convention as the Deity has no gender and is a spiritual concept so elevated, so perfect, so grand, that no human mind can encompass it.

So feel free to use the word "God", because whatever word you may use, this is simply a convention. Always bet on the intelligence of your readers. However, your readers will understand you best if you use the most appropriate word for the concept you wish to address. That's the most important thing writers much achieve : convey a message and for that, be as clear as possible for their readership.

Sorry about the long explanation but that's an interesting and inspiring question that you asked.