I heard him say that on occasion, but I didn’t think he was serious.

The words mean that the person said something (an opinion or belief), but did not say it often.  So, that person was not believed (or taken seriously).

[我偶爾聽他那麼說，可是我不認為他是來真的。]

句中 on occasion 做副詞用，意思和 sometimes, but not often 相同。當某個人態度認真，所言不虛的時候，我們可以說：He was serious.