One of the cats sleeps?
It’s one of the cats that sleeps, so it’s singular, therefore sleeps. It’s not all the cats that sleep. I know it’s a slightly awkward sentence in English however.
Can it also be said as " En om katterna sover"?
I don't understand why the word "one" can be en OR ett. I thought one was ett in Swedish. In this sentence it is a particular number called for, not an article.
Because it is a en-word, en katt. Ett av barnen sover. "One" agrees in gender with the noun it refers to.
"Ett" is the generic counting form, true, but the second it's describing a particular object, it has to agree in gender.