Correct spelling, explanation: we spell this word without doubling t, because adding the suffix doesn’t change the pronunciation. In English double consonant often follows a short vowel, because the pronunciation changes (for example: bitter and biter). In this case, therefore, it is correct to spell outer, not outter.

Definition of outer:
adjective, on the external part
Have you seen “Plan 9 from Outer Space”? It’s such a silly horror it is funny!

Incorrect spelling, explanation: outter is incorrect, because additional t is unnecessary – it simply doesn’t change anything. By adding the suffix -er we don’t change the pronunciation of this word, so the correct form is outer. For example, the word inner needs a double consonant, because it follows the short vowel, and thus word iner would be pronounced the same way as liner. Out however has got long vowel before the consonant.