Correct spelling, explanation: 93rd is the correct form as in full-word form it is ninety-third. As you can see this number ends with rd, so the same suffix is used for the numeral form: 93rd. Other suffixes (-th, -st, and -nd) are also used only with numbers ending with these letters in written form (for example 21st – twenty-first, 42nd – forty-second, 54th – fifty-fourth). Therefore 93th is the wrong form.

Definition of 93rd:
numeral, the ordinal number between 92nd and 94th
It was our uncle’s 93rd birthday last week.
This year there is a party in our town on the 93rd anniversary of its founding.

Incorrect spelling, explanation: this form can’t be correct because written form ninety-third ends with rd. Thus such suffix is used in the ordinal form written as a number: 93rd. 93th is wrong because -th can’t be found at the end of the word, and this suffix applies only to numbers ending with th (for example 76th – seventy-sixth). 93rd is the only correct option.

Incorrect spelling

Incorrect spelling