This is indeed a dialectal feature of American English found especially in the Appalachian South, typically in rural areas among speakers of lower social status. I just happen to have a book on American English that describes this dialect feature rather nicely. From page 4 of American English 2nd Edition by Walt Wolfram and Natalie Schilling-Estes:
In rural dialects of the United States, including in Southern
Appalachia, some words that end in -ing can take an a-, pronounced
as uh, attached to the beginning of the word (Wolfram 1980, 1988).
We call this the a-prefix because it attaches to the front of the
ing-word. The language pattern or "rule" for this form allows the a- to attach to some words but not to others.
That quoted section is from the beginning of an exercise on how to determine the patterns/rules of a dialect feature. It goes on to guide the reader through an analysis for determining the patterns/rules that govern a-prefix usage. If you're interested in the details I can add them to this answer. The general pattern of usage is described on pages 373-374 of the same book:
An a-prefix may occur on -ing forms functioning as verbs or as
complements of verbs as in She was a-comin' home or He made money
a-fishin'. This form cannot occur on -ing forms that function as
nouns or adjectives. Thus, it cannot occur in sentences such as * He
likes a-sailin' or * The movie was a-charmin'. The a-prefix may be
used to indicate intensity, but it does not appear to have any unique
aspectual marking analogous to habitual be or completive done. It
is associated with vernacular Southern mountain speech but is found in
many other rural varieties as well. To a lesser degree, an a-prefix
also can be attached to other verb forms, such as participles in
She's a-worked there or even to simple past forms as in She a-wondered what happened.
I also have personal experience with this dialect feature; one of my parents is from a very small town in northern Georgia near the Appalachian Mountains and occasionally uses a-prefixing. I don't believe it adds any meaning whatsoever to an utterance, but it does mark the speaker regionally and culturally (Appalachian South, rural background, likely lower sociocultural status). In other words, when you come across this a-prefix in something you read, you can omit the prefix from the sentence without any meaning being lost. One last quote from American English 2nd Edition suggests that this dialect feature may be a "holdover" from when it indicated "ongoing action":
"...speakers of some historically isolated Southern varieties such as
Appalachian English may retain an a-prefix on -ing verbs (*She was
a-huntin' and a-fishin') even though this prefix, which used to
indicate ongoing action, has long since vanished from standard
varieties of English."