Correct spelling, explanation: this word is the correct form, because of the way we create person-nouns in English. Here we have a verb write, which ends with e, so to create a noun meaning a person who writes we add -r to the word and we receive writer (normally we would add -er but the verb already ends with e). Therefore writer is the correct form, and there is no need to double the t, so writter is incorrect.

Definition of writer:
noun, a person who writes literature, usually full-time and/or for a living
John is a writer, he has written 3 novels already.
In my opinion, he isn’t a very good writer, but he is very popular.

Phrases with writer:
writer’s block
I believe every writer suffers from writer’s block sometimes.

Incorrect spelling, explanation: writter is incorrect because we do not have a reason to double the t since it’s in the middle of the word: write. To create a noun with the meaning of a person, we add, among others, the suffix -er (just like in teacher, and driver). Thus writer is the correct form. It is simply write and ending -r (e is already in the root word). Writer is therefore the correct spelling.