Contact me at 5 o'clock on a Monday in the new year
There are many resources which explain the rules about which preposition to use for time phrases to English learners, e.g.
- We use at with: with particular points on the clock; with particular points in the day; with particular points in the week; with special celebrations.
- We use on: with dates; with a singular day of the week to refer to one occasion; with a plural day of the week to refer to repeated events; ...
- ...
From the online Cambridge Dictionary
It seems to be a list of special cases. It doesn't look like there is one linguistic property that can be pointed to to classify at-times from on-times from in-times.
I am interested in how we came to use each of these prepositions for the time expressions that they are currently used for. Why do we not, for example, say "meet me at Monday"? This is interesting because looking only at present-day English, the rules about which preposition to use for which "type of time" seem arbitrary.