Note: the account below makes the claim that Hubbard Quarles was a son of John Quarles and Ann Grayson, but he appears to have been born at least a few years BEFORE their marriage in 1722/23. Needs additional research.
This essay, written on Hubbard Quarles & family of Brunswick County, Va, probably connects to your line -- it's my summary of some recent research on John & Ann (Grayson) Quarles and children. Let me know if this connects.
I'm guessing that the first Hubbard Quarles was the one who is in the early Brunswick County, VA, records. I have proof that he was one of four children of John
and Ann (Grayson) Quarles. The other three were 1) John Quarles, Jr. who married first cousin Ann Quarles (a daughter of James Quarles), 2) Elizabeth (Betty), whose will mentions John, Jr., and his daughter, Elizabeth Minor Quarles, and 3) Moses Quarles.
So here's the proof. From Winston of Virginia, pp. 445-446, "There was a John Quarles of St. George's Parish, Spotsylvania County, in 1723, 1726, & 1727...." Spotsylvania records: "On October 3, 1722, a marriage license was granted to John Quarles. The name of his bride is not given." "On September 30, 1723, John Quarles of St. George's Parish, Spotsylvania County, had patent for 417 acres in the said county on Massaponnax Run... (etc.)"
On April 16, 1724, John Quarles of St. George's Parish, Spotsylvania, sold to Richard Cheek of same, 70 acres, being part of a patent granted said Quarles September 30, 1723. Ann Quarles' right of dower in said land relinquished by John Waller, under power of attorney from her."
And from Cheek genealogy, "Robert Cheek first purchased land in Brunswick County, VA, in 1753. His property was located in northwestern Brunswick County, very near the border of Amelia (later Nottoway) County. Land records mention Rocky Run, Red Oak Creek, and the Nottoway River." Robert "... was a son of John Cheek of Essex and King & Queen Counties, and a nephew of Richard Cheek of "Beaufort" who lived in Spotsylvania County, VA, and later Beaufort County, NC. "
"Robert's neighbors in Brunswick included Hubbard Quarles and John Quarles. Hubbard and John Quarles of Brunswick, VA, were the sons of a John Quarles who was a neighbor of Richard Cheek during the 1720s - 30s in Spotsylvania County. Hubbard and John had a brother, Moses Quarles, who lived in Granville County, NC, during the 1750s-60s."
"Feb. 5, 1762, Brunswick Co., VA: Robert Cheek and wife Anne conveyed 150 acres to Hubbard Quarles, for 85 pounds, on south side of Nottoway River, beginning at the mouth of Rocky Run, adjoining land of Davis. Witnesses were Hugh Williams, Richard Caudle, and James Quarles. Ann Cheek relinquished right of dower (Brunswick Deed Book 7, p. 82)."
From Briggs family genealogy, "Richard Lanier (a child of Richard and Lucy (Briggs) Lanier) married Catherine Quarles, daughter of Hubbard Quarles, who left "negro woman Bess" to his daughter Katy Lanier in his 1779 will in Brunswick County. They were husband and wife as early as 21 February, 1771, when Quarles gave them 100 acres. They were later in Edgefield County, South Carolina."
And from a 1761 Granville County, NC, tax list of constable Ezekiel Hampton, the names Moses Quarles and Benjmen Hobord (Granville County, NC, Tax Lists, CR044.701, State of North Carolina Library & Archives, Raleigh).---
http://archiver.rootsweb.ancestry.com/th/read/Qualls-Quarles/2005-05/1117028393