You could use triannual (3 times a year) and triennial (every 3 years). However, it is more common to use phrases like "once every 4 months" and "once every 3 years" as the words sound almost alike but the phrases are very clear.

In three month intervals = Quarterly

True: it is technically possible to continue using the latin numbers (tri-, quad-, quint-, sex/hex-, sept-) for such examples, but in most cases you wouldn't use it for more than 2 or 3 times. It sounds too clumsy if you continue the pattern 'ad nauseam'.