1.Prepositional phraseIncidentally; 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."
2.AdverbIrrelevantly, off-topic.(Can we add an example for this sense?) (Should we delete this sense?)