Hope my answer will help you any further
I can already tell you that the use of the right preposition depends, so there are in a few occassions more than two correct possibilities.
At & On
At a time -> At dawn / At six / At midnight / At 4.30 Personally I remember the use of the preposition "AT" when it comes with a time indication when you are talking about a specific moment of the day or a specific hour. So, it is quite specific.
On a day or date -> On Monday / On 4 June / On Christmas Day When you are talking about a specific day, always "on"
Exceptions: at night, at Christmas, at Easter -> why "at" here ? Because the only thing mentioned here is a period and not a specific day
By a time/date/period -> at that time or before/not later than that date
other possibilities are:
on time/in time
on arrival/on arriving
at the beginning/at the end/in the beginning
in the end/at last/at first