Why is there an 'a" in front of swimming? It' s a noun .
the fish come a swimming to me
The fish come a-swimming to me > It is an archaism and should be spelt with a hyphen. It is often used in poetry to enable a line to contain the right number of feet.
Another example is from Waltzing Matilda:
Waltzing Matilda, Waltzing Matilda
"You'll come a-Waltzing Matilda, with me"
And he sang as he watched and waited 'til his billy boiled,
"You'll come a-Waltzing Matilda, with me