Correct spelling, explanation: this late Middle English word has its origin in Latin admittere, which meant – to send. Later, the meaning evolved and changed to the form that we know today. Admit is a rather formal verb, which in its base form has a single letter -t at the end.

Definition of admit:
1. verb – to accept something, say that something is true, especially when it’s something unpleasant,
She admitted that she’d forgotten his birthday.
2. verb – let somebody enter a place,
You can be admitted to this restaurant only with a valid Covid certificate.
3. verb – to go to a hospital because you need medical care,
The child was admitted to the hospital after a serious bike accident.

Expressions with admit:
The verb usually goes together with -to preposition so we admit to something. It can also be followed by the word that or the -ing form. Some examples:
He admitted to the mistake which ruined the whole project.
The president of the company admitted to taking the bribery, which shocked everyone.
He admitted that leaving this job was a rush decision, which he later regretted.
Some common collocations include: admit guilt, admit a charge, admit defeat.

Incorrect spelling, explanation: it is a common mistake to double the letter -t in a word admit. It probably comes from the fact that when we add the -ed or -ing ending to the base form we indeed double the -t letter, which results in such forms as admitted or admitting. The base form, however, has only one -t at the end so the form admitt is wrong.