What’s the gay male equivalent to a “mistress”?

When a married man regularly has sex with a woman who’s not his wife, the English language has a word for it. Any fluent English speaking reader knows that the woman is called a “mistress”. In recent years I’ve been spending some time in Thailand and I now know that there’s a similar word in the Thai language too, namely เมียน้อย which literally means “little wife”. In Thai, the male equivalent to a “little wife” might be a “little husband”, i.e. ผัวน้อย. But in English, calling a single gay man a “mister” if he regularly has sex with a guy in a gay relationship seems a bit odd to me. Can anyone think of a better word?