Correct spelling, explanation: 61st is the correct form because we need to use the same ending as in full-word form. Thus, sixty-first will be written as the number 61st, not 61th or 63rd. Other endings, like th, are used for ordinal numbers ending with th (for example fifth or ninth).

Definition of 61st:
numeral, the ordinal number between 60th and 62nd
– How old is your uncle? – It’s his 61st birthday tomorrow.
I was 61st on the list to get the tickets and I didn’t make it.

Incorrect spelling, explanation: this ending (th) is incorrect to use with the number 61, because the ordinal form of it is sixty-first, and the first is using ending st in its numeral form. Therefore 61th is incorrect, and this number should be written as 61st, because the word form ends with st. This is why the only correct form is 61st.

Incorrect spelling

Incorrect spelling