What does the phrase "come-a-courting" mean? The sentence is -

"He came-a-courting, and I said yes."
Regarding the prefix 'a-' before a present participle:
  1. (literary ( or archaic) (used before a present participle) in the act or process of⇒ ■ come a-running, ⇒ ■ go a-hunting
He courted me, and I accepted.
Look at meaning #1 of "court" as a verb here: