Correct spelling, explanation: 23rd is the correct form because it ends with third, and as such, it has to end with the same letters as the written form. Therefore twenty-third is 23rd, not 23th, just like twenty-fourth is 24th, not 24rd. Every number that is or ends with an ordinal number 3rd is written with the suffix -rd.

Definition of 23rd:
numeral, the ordinal number between 22nd and 24th
Do you know that it’s Monica’s 23rd birthday today? Send her best wishes.
It’s the 23rd time we visit North Spain this time of year. It’s our favourite place.

Incorrect spelling, explanation: this form is incorrect, because the word twenty-third (23rd) does not end with th, but with rd, so rd is the correct suffix for this ordinal number. We always add to an ordinal number a suffix from the written form, so in this case, 23th is incorrect, but the correct form is 23rd.

Incorrect spelling

Incorrect spelling