An opportunity or occasion; a chance to do something (often used with 'ついでに' to mean 'while you're at it').
買い物のついでに郵便局に寄ってきます。
I'll stop by the post office while I'm out shopping.
駅に行くついでだから、その手紙を出してきてくれない？
Since you're going to the station, could you mail that letter on the way?
旅行のついでに友人の家を訪ねた。
I visited a friend while I was traveling (as a side trip).
医者のついでに薬をもらってきてください。
Please pick up the medicine while you're at the doctor.
Archaic: order or sequence (original meaning); rarely used in this sense in modern Japanese.
古い文書では『序で』が物事の順序を表す語として使われている。
In old documents, '序で' is used to indicate the order of things.
Archaic: a term meaning a successor; found in historical contexts and rarely used today.
古記録には、家督の序でが誰に渡るかが書かれている。
Old records state to whom the family's succession (order) was passed.