As you know, the usual preposition for days is 'on', used for calendar dates, days of the week, etc. So you might use the phrase 'on a particular day' to mean Monday as opposed to Tuesday, or the first day of the month as opposed to the last.
'In a particular day' has a different meaning, because it means throughout the day, or over the course of the day. So you might say 'I can read a short novel in a day', meaning that you can read the novel within the time period from when you get up until when you go to bed.
Another use of 'in' with day would be in a sentence such as 'Hamsters are nocturnal: they are awake at night and asleep in the day'. Again, that means during the period from dawn to dusk, and we are talking about what happens 'within' that time span.