Definition of "by the way" in English

Prepositional phrase

1. Incidentally; used in referencing a parenthetical statement not timely, central, or crucial to the topic at hand; foregone, passed by, something that has already happened.

   • His mother will be coming for dinner tomorrow, and, by the way, she recently sold her collection of ceramic eggs.

Adverb

1. Irrelevantly, off-topic.(Can we add an example for this sense?)