1.  Marriage Record:

2.  Anon.  1915.  Encyclopedia of Virginia Biography.  Richmond, VA (online at Ancestry.com):

II--Colonial Presidents and Governors  Name: Jenings Edmund president of the council and acting governor from June, 1706, to August, 1710, was son of Sir Edmund Jenings, of Ripon, Yorkshire, England, and his wife Margaret, daughter of Sir Edward Barkharn, lord mayor of London, 1621-22.  He was born in 1659, and died June 2, 1727.  He came to Virginia at an early age, and settled in York county.  He was appointed attorney-general in 1680, and retained the office till after 1692.  He was appointed to the council in 1701, and remained a member till his death.  In 1704 he was appointed secretary of state, and from June, 1706, till August 23, 1710, he was acting governor. Later, after the death of Hugh Drysdale, he would have again become acting governor, but was set aside on account of his feeble health.  He married, Frances, daughter of Henry Corbin, of Buckingham House, and had issue (1) Frances, married Charles Grymes, of Moratico, Richmond county, and was ancestress of General R.E. Lee; (2) Elizabeth, married Robert Porteus, of New Bottle, Gloucester county, who afterwards removed to England, where she became the mother of Beilby Porteus, Bishop of London; (3) Edmund, secretary of Maryland, married in 1728, Anna, widow of James Frisby and Thomas Bordley, and daughter of Matthias Vanderheyden, by which marriage he was father of Ariana (who married John Randolph of Virginia, father of Edmund Randolph, first attorney-general of Virginia and of the United States)...

3.  Email from Jean Purdy:

The parents of the above are Sir Edward Jennings [born] Ripon, Yorks 30 Nov 1626 — he was an MP...  Gov Edmund’s mother was Margaret Barkham [born] C 1626 in Tottenham — she was indeed the daughter of Sir Edward Barkham, but the 2nd Baronet who was an MP and married Frances Berney.  Margaret was the granddaughter of the Lord Mayor.  The latter did have a daughter Margaret, but she was born in 1495 — married Sir Anthony Islay and was buried in 1640 at All Hallows, Tottenham.  The Barkham Home was in Tottenham, Middlesex (Crokes Farm House} and a country home at Southacre, Norfolk...

4.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).  Sources there overwhelmingly give Edmund Jr.'s wife given name Ariana, not Anna.