Rambling Boy is classified by Laws as "The Wild and Wicked Youth" [Laws L12]. The English folk song dates to before 1830 (broadside, Bodleian Harding B 25(2054)). Here's info from the Ballad Index:

REFERENCES (18 citations):
Laws L12, "The Rambling Boy (Wild and Wicked Youth)"
Belden, pp. 136-137, "The Rambling Boy" (1 text)
Randolph 148, "The Rambling Boy" (2 texts, 1 tune)
Warner 101, "The Rambling Boy" (1 text, 1 tune)
Sharp-100E 83, "The Robber" (1 text, 1 tune)
Fuson, pp. 63-64, "The Rich Rambler" (1 text)
Cambiaire, pp. 43-44, "The Wretched Rambling Boy" (1 text)
Ritchie-Southern, pp. 91-92, "The Reckless and Rambling Boy" (1 text, 1 tune)
Combs/Wilgus 90, pp. 184-185, "The Rich and Rambling Boy" (1 text)
Kennedy 326, "Newlyn Town" (1 text, 1 tune)
OLochlainn-More 35, "The Newry Highwayman" (1 text, 1 tune)
Zimmermann p. 96, "The Bold and Undaunted Youth" (1 text fragment)
BrownII 121, "The Rambing Boy" (1 text)
Lomax-FSNA 96, "The Ramblin' Boy" (1 text, 1 tune)
Cohen/Seeger/Wood, pp. 130-131, "The Rambling Boy" (1 text, 1 tune)
Thorp/Fife XIII, pp. 148-190 (29-30), "Cow Boy's Lament" (22 texts, 7 tunes, the "L" text being in fact a version of this piece)
Darling-NAS, pp. 106-107, "The Rambling Boy" (1 text)

RECORDINGS:
O. J. Abbott, "The Bold and Undaunted Youth (The Rambling Boy)" (on Abbott1)
Clarence Ashley & Tex Isley, "Rude and Rambling Man" (on Ashley01)
Justus Begley, "The Roving Boy" (AFS, 1937; on KMM)
Jumbo Brightwell, "Newry Town" (on Voice03)
Carter Family, "The Rambling Boy" (Bluebird B-8990, 1941/Bluebird 33-0512, 1944)
Wade Mainer, "Ramblin' Boy" (Bluebird 33-0512, 1944)
New Lost City Ramblers, "Rambling Boy" (on NLCR05)
Riley Puckett, "Ramblin' Boy" (Columbia 15605-D, 1930)
Bob Scarce, "Newlyn Town" (on FSB7)
BROADSIDES:
Bodleian, Harding B 25(2054), "The Wild and Wicked Youth," T. Birt (London), 1828-1829; also Firth c.17(208), Harding B 11(576), Harding B 15(376a), Harding B 11(939), Firth c.17(6), Harding B 16(307a), Harding B 11(4205), Harding B 11(4211), Harding B 11(4212), Firth b.34(314), Harding B 11(3519A), Firth c.17(7), 2806 c.16(325), Harding B 17(338a), Harding B 20(117), Harding B 17(337b), "The Wild and Wicked Youth"; Harding B 28(235), "The Highway Man's Fate"; Harding B 26(67), "The Bold and Undaunted Youth" ("In Stephen's-green I was bred and born"), J. Moore (Belfast), 1852-1868

ALTERNATE TITLES:
The Rake and Rambling Boy
Adieu Adieu

Notes: The Bodleian "The Wild and Wicked Youth" broadsides, and OLochlainn-More 35, include a version of the lines
"I robbed Lord Mansfield I do declare, ...
Lord Fielding's gang they did me pursue And taken I was, by that cursed crew."
The Bodleian notes to 2806 c.16(325) include references to the cast of characters: "Fielding, John, Sir, d. 1780; Mansfield, W.R., Baron Sandhurst, 1819-1876"
Broadside Bodleian Harding B 26(67) is another example of the "I robbed Lord Mansfield I do declare" group. Zimmermann's fragment seems to be from this version. In this case he falls in with "Fieldskin gang." - BS
Given the date of the song, I would think the Mansfield involved more likely to be William Murray, first Earl of Mansfield (1706-1793), who was Lord Chief Justice of the King's Bench from 1756. This has at least sometimes been corrupted to Lord Melbourne, presumably William Lamb, second Viscount Melbourne (1779-1848), the Prime Minister (on and off) from 1834 to 1841. But Mansfield is closer to the Era of the Highwaymen -- and, as Chief Justice, someone they would doubtless enjoy taking.
Fielding in fact might refer to John Fielding or his brother Henry, the author (died 1755). Henry Fielding was driven by poverty to take a post as Commissioner of the Peace for Middlesex in 1748. John Fielding, despite being blind, succeeded him in 1754 -- and dramatically improved law enforcement, though he didn't have the funding to carry out all his reforms. Still, he did enough that life became much harder for the highwaymen.
"Fielding's Gang" is presumably the Bow Street Patrol, founded by the Fieldings as the first almost-national police force in England.


RAMBLING BOY- Carter Family 1941

I was rich but a rambling boy
Too many a city I did enjoy
And there I married me a pretty little wife
And I loved her dearer than I loved my life

She was pretty both neat and gay
She caused me to rob the road highway
I robbed it yes I do declare
I made myself ten thousand there

Plenty dry goods for to carry me through
My pistol, sword, my money too
My forty-four she never failed
My true love comes for to go my bail.

My mother says she has no home
My sister says she's all alone
My wife she's left in sad despair
With a broken heart and a baby fair.

Now when I die dont bury me at all
Just place me away in alcohol
My forty-four lay by my feet
Please tell them I am just asleep