Correct spelling, explanation: this form, 41st, is correct, because ordinal numbers end with the same suffix as their word-form ending. Therefore forty-first will be written as 41st, seventy-fourth as 74th etc. This means that 41th is incorrect and the correct form is 41st.

Definition of 41st:
numeral, ordinal number between 40th and 42nd
For my dad’s 41st birthday we are going for a trip to Cracow.
This is a very small private school; Jack was admitted last week and he is 41st student there.

Incorrect spelling, explanation: 41th is a mistaken way to write this ordinal number, because th is not an ending for numbers ending with first. The correct suffix for first is st. Thus 41st is the correct form here. In case of numbers ending with th in pronunciation, like ninth or sixteenth, the ending would be th, but for forty-first it is 41st.

Incorrect spelling

Incorrect spelling