Correct spelling, explanation: the word permitted is a past participle and a past simple form of the infinitive to permit. It is made of a basis and a suffix. There is a rule in the English language that when we have a single vowel before the last and stressed consonant in a word, we need to double that consonant. Although, many people forget that rule. That’s why the correct form is permitted and the incorrect one is permited.

Definition of permitted:
1. verb (past participle, past simple), officially allow (someone) to do something
My mum permitted dogs in the house.
His means permit him to live comfortably.
2. adjective, allowed or tolerated
Smoking is not permitted in the cinema.
Visitors are not permitted to take photographs.

Collocations with permitted:
Some most commonly used collocations include: legally permitted and normally permitted.
Abortion is legally permitted in this state.
Development is not normally permitted in conservation areas.

Incorrect spelling, explanation: permited is a spelling mistake because it doesn’t consist of the double -t letter, which is necessary in this case. Permit is a regular verb, which means that its conjugation shouldn’t be problematic to anyone. You need to add the suffix -ed to the end of the root. Although, we have to remember one principle: when there is a single vowel before the last and stressed consonant in a word, this consonant must be doubled. That’s why permitted is correct and permited is not.