The fiddle tune that is popularly known as The Red Haired Boy goes by several other names, but when the title changes, the words do too.
I first heard it called The Little Begger Man and sung by Ian and Sylvia;
"I am a little beggerman a begger I've been
For three score or more on this little Isle of green."

I've heard Jamie Snyder sing a Newfoundland version called The Old Ragadoo:
"I'm a hearty Newfoundlander Michael Chaser is my name
I was born on Green Island I'm a fisherman by trade."

John Carter remembers his dad, from the Ottawa Valley singing The Old Soldier With The Wooden Leg:
"There was an old soldier and he had a wooden leg
And he had no tobacco so tobacco he would beg."

I've heard some contemporary singer/songwriters use this tune for songs of their own - Washboard Hank has one that I can't recall right now.

The tune is sometimes called Gilderoy, which is a anglicized version odf the Irish for Red Haired Boy.