Most databases give the father of Elisha Harrison as John Harrison. This is incorrect.
Then Jonathan Harrison is said to be the son of John Harrison (1716-1776) and Susanna Edmunds (1720-1771) but I have no proof of that relationship. If he was, he was born perhaps 2 Apr 1745 in Sussex Co, VA. [I actually found that John Harrison & wife Susannah had a son baptized Albemarle Parish, Sussex, on this date - his name was John, not Jonathan.] Old family documents have indicated Jonathan's father was an Elias Harrison - no proof offered.
Mercy Terry was the daughter of William and Rachel Terry of Botetourt County, VA. Records of the estate of William Terry [died1808] from 1808 reveal that "Mercy Terry, wife of Jonathan Harrison" received her one/eighth share in her father's estate.
Mr. Bunton descends from William Canady Harrison, a grandson of William & Rachel Terry Harrison through their son, Elisha Harrison. He has a family letter stating that Elisha H. Harrison's father was Elisha [Elisha H. was a brother of William Canady and my ancestor Nathaniel Harrison]; his grandfather was Jonathan Harrison; his great-grandfather was Elias Harrison. The grandmother Harrison was a Terry. The letter also mentions a second cousin named Joseph Terry who lived in Madison Co KY - there was a Joseph Terry in the 1850 Madison Co KY. This Joseph Terry was a grandson of John Terry, brother of Mercy Terry; thereby proving that that Elisha H. Harrison did have a 2nd cousin named Joseph Terry.
Online information concerning Jonathan Harrison is confusing and cannot all be correct.
There is the suggestion of a Jonathan Harrison, Jr. - so some of the above records could have been his, but certainly both Jonathan and Mercy were alive as late as 1809.
Some state that Jonathan or John "Jack" Harrison was a Longhunter - this may be a confusion with another John "Jack" Harrison who was at Ft. Boonesborough but is Not the father of Elisha. I don't think there is any proof that the Longhunter was the either a Jonathan, or was the son of John Harrison of Sussex/Surry in Virginia.
The Harrison Y-DNA study indicates no relationship between descendants of the Harrisons from Sussex/Surry and descendants of Jonathan Harrison & Mercy Terry. However, only two descendants of Jonathan & Mercy have been tested - they do match each other.
A John Harrison filed a will in the County of Sussex, VA in 1776, the year he died, leaving his land and leases in Surry Co to his son William Harrison(1747), along with several slaves, livestock, tools, and household items. The will of 1776 also mentions daughters Mary Peebles married to Thomas Peeples, Lucy Adkins, and Betty Mason, deceased, who had been married to James Mason. There are baptisms in Albemarle Parish (Surry Co before Sussex was formed in 1754) for Lucy, Elizabeth (Betty), William, and the John mention above, but not daughter Mary. Neither a son John nor any descendants of a John were mentioned in the will which might indicate he was not living and had no issue.
Mercy's parents were William and Rachel Terry.
There exists a sale bill for the estate of William Terry, 13 Dec 1744, in Augusta Co VA - obviously an earlier person of this same name.
Records of the estate of William Terry in Botetourt Co VA name 8 children including "Mercy Terry, wife of Jonathan Harrison". The other children were William who married Patience, John born 1760 who married Esther Brown, Miles who married Hannan Horton, Susannah who married Thomas Brown, Jasper who married (1) Ruth and (2) Margaret Snidow, Rachel who married John Martin and Jemima who married Ezekial Boucher.
JONATHAN HARRISON and MERCY TERRY had the following children: