You would have to check in a VA Library to obtain records on Adcocks who served in the Rev. War.It definitely would not have been the first Joseph of Essex Co., VA as he was not yet 21 in 1719 when his father John Adcock died. That Joseph was, however, married by 1730 and he and his wife Elizabeth Bryan were buying and selling land in Essex Co., VA. in the 1730's. That Joseph was the son of John Adcock (who died in 1719) and Mary Beland who was the daughter of Joseph Beland - hence the only son named for his maternal grandfather - a fact that was listed in the deed records in Essex Co., VA- land inherited from Joseph Beland "his grandfather on his mother's side."
The Joseph born in 1727 would have been that first Joseph's son. He would have been born in Essex Co., as his father and mother were still in Essex Co., VA in 1743 - or at least that is when they sold their last bit of land.By the 1780's there were at least three Josephs in that family who would have been old enough to fight in the Rev. War.There were at least three Edmund Adcocks by 1800 paying taxes.They were all still in Buckingham Co., VA (formed from Albemarle I believe- I don't have my notes in front of me) in 1800, and that is what most researchers miss - they were still in VA.
There were also two Edmund Adcocks in North Carolina by the 1780's who had come to NC from Essex Co., VA prior to 1750.These also came from Essex Co., VA.Henry Adcock, son of Edward Adcock of Essex Co., VA who died early 1700's and Henry also dying in EssexCo. in 1733 had two sons John Adcock (from whom I descend) and Tobias Adcock (Tobias named for his maternal grandfather Toby Smith as Edward Adcock was married to Elizabeth Smith who had a brother Henry Smith).John and Tobias, sons of Henry, came to N.C. and were paying taxes in N.C. by the 1750's - John actually owning land in Granville Co., NC in the 1740's.Toby Adcock had at least two sons, Edmund and Henry.Edmund never left N.C. and died in N.C. around 1800 as his will is here in 1801 or 1802.Edmund also had a son Edmund (sometimes spelled Edmond) who left N.C. and moved south sometime after 1790.He had three sons prior to leaving NC according to the first census. He was not associated with the Edmunds who were in Buckingham Co., VA though they were distantly related from Essex Co., VA.One of Edmund's other sons also had an Edmund in N.C. who married in N.C. Edmund of N.C. did have a son Joseph Adcock who was born in N.C., fought in the Rev. War from N.C. and died in N.C. in Chatham Co.When his father, Edmund Adcock sold his land in Granville Co. around 1781,he moved near two of his sons in Chatham Co., NC.That is where Joseph died.Joseph had several sons and they are named in his will.His great uncle John whom I call "old John" stayed in Granville Co., died there in 1780 and had sons who were too old to fight in the Rev. War except for several of the younger ones, one of them Edward Adcock (my fourth gr. grandfather) who also died in N.C. in 1799. Several of "old John's" grandsons fought in the Rev. out of Granville Co., NC"Old John" Adcock had grandsons to move to southern NC, S.C., TN, and GA.
I gave you the latter information, as I believe the Edmund in GA was related to the N.C. Edmund.It was later before one of the Buckingham Co., VA Edmund Adcocks moved to GA.
Since all of Buckingham Co., VA records were destroyed (except for tax records - which are very revealing) we don't have most deed records in the mid 1700's. However, the tax records show they were still in Buckingham Co., VA.
My research is from hours of reading original clerk records in Essex Co., VA, York Co., VA, and in numerous counties in N.C. - most of the records in northern and central N.C. are intact, and from N.C. Archives. If any of the Joseph Adcocks of Buckingham were in theRev. War, and there are pension records, they should be available either in Richmond or D.C.