Correct spelling, explanation: the word permitted is a derivative of the verb permit. As you can see, it contains a double -t letter. If you’re wondering why here’s the crucial rule: we need to double the final letter when a one-syllable verb ends in consonant + vowel + consonant. Many English users tend to forget about this principle and spell this kind of verb with just one consonant. Permited is not correct.

Definition of permitted:
1. verb (past participle, past simple), to make something possible
I permitted myself to be angry just for a minute.
My girlfriend permitted me to buy her an expensive gift.
2. adjective, allowed
Playing loud music is not permitted after 10 pm.
Before you rent this apartment, make sure that keeping pets is permitted.

Collocations with permitted:
Some most commonly used collocations include: be permitted to do something.
I’m legally permitted to shoot.
I’m grateful you have permitted me to return home.

Incorrect spelling, explanation: the most common way of creating regular past simple/past participle forms (and also the adjective participles) is adding a specific suffix (-d or -ed) to an unchanged root (the verb). It’s worth remembering that sometimes we must do one other thing: double the last consonant of the root when there is a single (and stressed) vowel before the last consonant in a word. That is the reason why this word should be spelled as permitted, not permited.