「昨日のこの時間には寝てました」って英語でなんて言うの？

1) I was already resting by this time yesterday.
'Resting,' is another common way to say asleep, it is used interchangeably with sleeping, napping, etc.

2) I was sleeping long before this time yesterday.
Saying 'long before' is a well-known, shorter way of saying 'at this time,' or 'at the same time.'

3) This time yesterday I was fast asleep.
'Fast asleep' is a very common phrase meaning deep sleep.

"At this time" notes the time in which the action happened. "Already" means that something has happened and "asleep" is good to use because that is the way that we say that you were sleeping.

I hope that this helps :)

"At this time yesterday, I was already sleeping."

"I was asleep at this/that time yesterday." (This time - at the time you are talking today, or that time - a time that someone has mentioned.)

At this time - this could mean 8 pm, 9 pm, etc.

Already - meaning before the time that was mentioned.

If you are in the land of nod it means that you are asleep. Yes, it seems clear you were sleeping this time yesterday.

To explain that you were asleep at this time yesterday, you can say:
"I was already sleeping at this time yesterday."
"Yesterday, I was asleep at this time."

If you are talking about something happening at the same time then you would say 'at this time' or 'by this time'
already means something that has happened before