meaning - What does the “a’ ” in “a’blowing” signify？

Wikipedia says the a- prefix is used to form a predicative adjective with progressive aspect.

OED gives a dozen or more origins/meanings for the a- prefix, but I must admit I can't see any there that really correspond to OP's examples except #11, where it says the force of the prefix is so little apparent, that the derivatives in a- hardly differ in sense (in respect of, say, rise/arise, wake/awake).

So I think in OP's particular examples, the a- prefix either means nothing at all (effectively OED's take), or it can be seen as replicating/emphasising the progressive aspect of the verb (which is also being done by the -ing "suffix" anyway).

The apostrophe in OP's case is arbitrary (you could replace it with a hyphen, or nothing at all).