Correct spelling, explanation: if you want to create an ordinal number in English language, you must add a specific ending to a number. Most of the time they consist of a number followed by the suffix -th (for example, let’s take eighty-fifth). It is different with the first three numbers. Number three transforms into third, not thirth.

Definition of third:
numeral, a number that comes between second and fourth
I don’t want to be third, I want to be first.
I think it’s your third job this year.

Incorrect spelling, explanation: ordinal numbers in English are formed by adding the appropriate ending to the number. The most common suffix is -th (for example, fourteenth, twenty-fifth, and forty-eighth), but when it comes to the number three, the ending is -rd. The word thirth is therefore a mistake and third is the only correct form.

Incorrect spelling