Correct spelling, explanation: ninth is the correct form of writing down the ordinal number of 9. We add the suffix th to the number nine with the omission of e to create the correct spelling. That is why the spelling nineth is not correct, because of the vowel e that was not left out. The only correct version is ninth.

Definition of ninth:
adjective: being the ordinal number of nine;
Jenny was the ninth person on the admission list.
Noun: the ninth part;
The inheritance was divided among all the grandchildren, so Julie got the ninth part of the fortune.
Adverb: in the ninth place;
Because of the foot injury, he was in ninth place in the Olympic qualification and lost his chance to fulfill his childhood dream.

Incorrect spelling, explanation: nineth is the mistaken spelling of the ordinal number ninth. The vowel e should be omitted when we create this word by adding suffix th to the number nine. It is an easy mistake to make, so we should remember that only spelling ninth is the right one.