Correct spelling, explanation: the word admit entered English in the times of Middle English and it derives from the Latin word admittere, which used to mean to send. It is worth noticing that today in its basic form the word admit features a single -t letter, which doubles only when we add the -ed or -ing ending.

Definition of admit:
verb – to agree, especially unwillingly, that something is true,
He finally decided to admit that it was his mistake, not mine.
verb – to let someone enter a place,
They will admit you to this restaurant in formal clothes only.
verb – when a person or a country is allowed to join some organization,
Next year our country will finally have the right to admit to the European Union.
verb – when a person goes into the hospital because he or she needs medical help,
After the accident, the hospital had to admit her immediately.

Collocations with admit:
Some typical collocations include:
admit defeat – when you accept that you failed,
He could do nothing but admit his defeat, but still left the court with his head up.
be forced to admit – when you have to admit to something,
She was forced to admit the truth.
refuse to admit – when you don’t want to admit to something,
They refused to admit that it was their mistake.

Incorrect spelling, explanation: the spelling of the word admit causes some troubles as when you add some ending to it, e.g. -ing or -ed, you need to double the -t letter at the end, which gives admitted or admitting. Because of that, however, many users of English think that there is also a double -t letter in the base form, which results in a common mistake of spelling the word as admitt.