Incorrect spelling, explanation: an adverb quarterly is derived from a word, functioning as a noun or adjective quarter and a suffix ly. This is the reason why the only correct form is quarterly, not quaterly. Therefore, learners should remember to write r at the end of two syllables of this word. The second reason is its origin. It comes from Latin as quartarius meaning the fourth part. In English, it has been used since the 15th century and nothing has changed. As a result, quaterly is incorrect.

Correct spelling, explanation: this word functions as an adverb and can be divided into a noun quarter and suffix ly. Quarter means one-fourth of something and it is spelled with r at the end of both syllables. However, the British do not pronounce this consonant and sometimes can forget to write it. That does not change anything. The correct form is quarterly with r, not quaterly.

Definition of quarterly:
adjective/adverb/noun, done, produced, or appearing four times a year;
You should pass the test quarterly to be our worker.
This magazine occurs quarterly.
They decided to take the income quarterly.