I think that "in the morning" is much more common than the others. Example: I go to school in the morning In this example, "in the morning" is a prepositional phrase. When I try to think of examples of "on" or "at" being used, I can only think of examples where "morning" is functioning as another part of speech such as an adjective or adverb. Example: I go to school on the morning bus. Example: I saw her at the morning session.

The correct one is "in the morning." The others don't really make sense, because "on," when used to reference time, usually indicates a particular, more focused span of time (ex; "on the hour of..."). Using "in" makes it more broad and general and can refer to any moment within/during the morning hours. "At" is used sometimes temporally, but not nearly as often as "in." (ex; at night). To make the explanation even simpler, "in the morning," is simply a set phrase and it usually doesn't change form. Additionally you can say "in the afternoon," or "in the evening." Exactly why it's this way, I'm not sure how to explain, but there phrases are very concrete. I hope this helps. If you have further questions, let me know.

The only one of those that is correct is "in the morning." Both "on the morning" and "at the morning" are wrong, you would never use either of them in modern English. Therefore you would say "I joined a monthly meeting in the morning."

yes we can also say on the morning, here is a link if you want to know a little bit more about this expression https://www.linguee.es/ingles-espanol/traduccion/on+the+morning.html.