Dates preposition confusion

I'm a bit confused about the dates preposition. I know a date can be said in two ways, for example "the second of March" and "March 2(nd)". But now I seemed to a bit more complex date like (September 10, 2019). For this date which preposition "in" or "on" should be used? [in September 10, 2019] or [on September 10, 2019]?

I can understand why you find this a bit confusing, different prepositions are used for time as the time period becomes shorter and more precise. With periods longer than a day the preposition used is "in". For instance: "In the 21st century", "In 2020", "in September 2020", "in the first week of September 2020".

When we get to a range of days we sometimes say "in" but sometimes say "between" if the dates are specified. Again for example "In the first three days of September 2020" but "between the 2nd and the 5th of September 2020".

When we are talking about a single date we say "on" because a single date is a distinct period. That is we say "on the 2nd of September 2020".

With precise times within a day we say "at", for example "at 13:04 on the 2nd of September 2020". When the time periods are less than a day but are not precise we again use "in" or "between", for example "in the first hour of 2nd of September 2020" meaning at some time in the range 00:00 to 01:00 or "between midnight and 1:00am on September 2nd 2020" meaning the same thing, but you should notice that the preposition for the day is "on".

If we are less sure of the time, even for quite extended periods, we sometimes say "around" so you get "At around 1:00am on the 2nd of September 2020". or "around the end of August 2020" or even "around 2010".

The same prepositions are used for very short periods of time as well if we have enough information. For instance with a computer batch run we can sometimes say "That record was processed in the first 100 milliseconds of the run".