Is "tri-quarterly" a real English word meaning 3 times a year?

If "tri-quarterly" means anything, surely it would be every third quarter (every nine months). Or possibly three times a quarter, which is monthly. You can't redefine a quarter as a third, though.

Three times a year is triannual — not triennial which is every three years. You could also say every four months; "every four months" is preferable because it removes the possibility of confusion between triennial and triannual.

A word that I find used a lot is: tertial

Tertial is a foreign word from Latin meaning a third . In the temporal sense, a third is understood to mean a third of a year , i.e. a period of four months .

Trimester Trimester · Academic term, a trimester system divides the academic year into three terms