The preposition on is used in connection with "day","on this day" parallel to German "an diesem Tag".
"on" is also used with days of the week, which contain the word day: on Monday, on Tuesday, and on weekdays.
"on" is also used when "day" is connected with "morning/night": on Monday morning, on Saturday night.
When "morning, afternoon," is used alone then the concept of period of time prevails and "in" is used: in the morning, in the afternoon.
"night" can be used with a lot of prepositions: at night, by night, during the night.