Thanks Rob! I'm actually looking for a quite informal, even slang phrase for that. And I also need to know whether "are you sleeping yet" is archaic or not.

It's not archaic, but it would be more common to ask, "...are you asleep yet." By the way, "Anglo-Saxon" refers to a specific ethnic sub-group of people in the British Isles. The "English speaking world" would more appropriately reflect the diversity of the people who speak the language today in places all around the globe.

thanks Gray😀

I agree with Rob's answer -- "You asleep?" would be the casual, informal way of asking if someone is asleep yet. I don't know if "sleeping yet?" is archaic, exactly. I can imagine someone asking this in modern-day English. It's not the most natural thing to say, but it doesn't sound archaic to me. If you add the pronoun and say "You sleeping yet?" it sounds perfectly modern. I think the reason it sounds a little weird to ask if someone is "sleeping yet" is because "yet" implies impatience. It sounds like you think the person *should* be asleep by now. But if so, why are you asking them a question about it? "You asleep" makes a bit more sense, because we usually use it to (quietly) find out whether or not someone is awake (e.g. if we want to ask them a question, but don't want to wake them up if they're sleeping), OR to purposely wake them up ("Hey, you still asleep? Get up, we need to leave in five minutes!").

As a native English speaker, I've never heard "sleeping yet" used by itself. It'd be considered grammatically incorrect and an incomplete sentence because it doesn't include a subject noun. "Are you sleeping yet?" is the correct way to go. 👍