Incorrect spelling, explanation: this form is wrong because doubling t in this word is completely unnecessary. A double consonant often is placed after a short vowel in cases where pronunciation changes. In outer pronunciation doesn’t change, so we don’t have to double the t. This is the reason why outer is the correct form.

Correct spelling, explanation: according to the rule we double the last consonant in a word in cases when pronunciation changes (for example we write inner not iner). In the same way, we don’t double t in outer, because there is no change in pronunciation, so it’s not needed. Outter is the wrong spelling.

Definition of outer:
adjective, situated on the outside, external
The outer walls we painted blue, which we surprisingly loved.