Which preposition should I use (during/on the time)

Context: Teachers set their schedules in an electronic calendar by showing the time slots they can teach. And we’ve noticed that these time slots are very popular among students. Which preposition should I use in these sentences:
"Students are really eager to schedule lessons during/on the time (slots) you set."
"Most students book lessons during/on the time you set."

I tried to google the information, but the only explanations I find are about "on/in time". I didn’t manage to find anything helpful.