Correct spelling, explanation: third is an ordinal number and it’s a derivative of the number three. The first three numbers in English are inflected differently from the rest. One becomes first, two becomes second, and three becomes third. The remaining ordinal numbers are formed by adding the ending -th to the number. We must not forget about this principle when spelling third. Thirth is a mistake.

Definition of third:
numeral, coming next after the second in position
My aunt took third place in the competition. We’re proud of her!
Your room is the third on the left.

Collocations with third:
Some most commonly used collocations include: third party, Third World, and the third year in a row.
I hope any of the third parties haven’t heard our conversation.
The USA should’ve dealt with crises in the Third World sooner.
This is the third year in a row that a debut novel has won.

Incorrect spelling, explanation: the -th suffix is added to most numbers when creating ordinal forms. The first three numbers are exceptions. Third and thirth are words that look very similar, so it’s easy to get confused. However, we must remember the aforementioned principle. This is why the form thirth is wrong and the form third is correct.

Incorrect spelling