Correct spelling, explanation: this ordinal number has its origin in Germanic languages, but Middle English already featured the forms nynthe and nynte, which are close to the modern version of the word. The word ninth is more commonly used as the number 9th.

Definition of ninth:
1. ordinal number – 9th written as a word,
It is the ninth case of the disease in this neighborhood.
2. noun – one of nine parts of something,
A ninth of 27 will be 3.

Collocations with ninth:
Some common collocations include: come ninth, rank ninth, fall on the ninth of a month
He came ninth in the race, which was rather disappointing.
She ranks ninth in the world championships.
The party falls on the ninth of June.

Incorrect spelling, explanation: the basic rule of forming ordinal numbers in English is to add the -th ending to a number. In some cases, however, the spelling changes. For example, when we add the -th to nine, the -e letter disappears, which gives the form ninth. Some English users are not aware of that and they spell the word as nineth, which is wrong.