Of A Meaning

(dated, now dialectal, idiomatic) on every; in the (followed by a noun indicating a certain time)

Example: 1839, John Gibson Lockhart, Memoirs of the Life of Sir Walter Scott, Bart:
  He always used to dine at my father's house of a Sunday.
2008, Kim Patrick, “Rewarding Good Behavior in Children”:
  So, next time they come to me of a morning and ask the same question, what do you think my answer might be?