Correct spelling, explanation: the word 21st is an exception. It ends with -st, because of the number one in it. If we hesitate before creating an ordinal number, we should write it down with words. Then we’ll clearly see if it ends with an irregular form, like first. When an ordinal number ends with number one, it’s spelled with the suffix -st (except for 11th).

Definition of 21st:
numeral, a number that comes between twentieth and twenty-second.
Do you like living in the 21st century?
I wonder when will be her 21st birthday.

Incorrect spelling, explanation: twenty-first is an ordinal number, which means it’s used to denote the order of something. When creating this kind of numeral, one must add a specific ending to the number. In the case of number one, it’s -st. That’s the reason this ordinal number is spelled 21st, not 21th.

Incorrect spelling

Incorrect spelling