The following material is from Francis Barnard (ca. 1616–1698) and his Descendants, A Genealogical Study, Part A, by Walther M. Barnard, Version of 09 August 2009, page 1. Used with permission.
The Early Barnard Settlers
Emigrating from England, Barnards were among the earliest settlers of New England. Although none were passengers on the Mayflower which arrived in December, 1620, bearing the Pilgrims which settled at Plymouth, Massachusetts, Barnards were immigrating within 14 years to New England. Listings of Barnard arrivals there in 1620 have been published, but these appear to be errors; they include arrivals to Connecticut and Cambridge, Massachusetts, some years before these localities were settled.
The following are listed as arriving in 1620, as cited in Banks, Charles Edward, Topographical Dictionary of 2885 English Emigrants: Baltimore; Genealogical Publishing Co., 1957 (all from Barnard, Roy, The New World Book of Barnards: Halbert’s Family Heritage, Ohio, 1997, p. 51–52):
Bartholomew, in Connecticut, p. 44; Bartholomew, in Maine, p. 100; John, in Cambridge, p. 42; John, in New England, p. 48; Methuselah, in Massachusetts, p. 138; Robert, in New England, p. 41, 150.
The very earliest arrival in the New World with the Barnard surname may have been a William Barnard, who, as a young man of 21 years, arrived in Virginia as early as 1622/23.
Boyer, Carl, 3rd, ed. Ship Passenger Lists: The South (1538–1825), Newhall, California: the editor, 1979—per Barnard, Roy, 1997, op. Cit., p. 52; “Lists of Living & Dead in VA, Feb, 1623.” Colonial Records of Virginia, 1874, Richmond, VA: R F Walker, 1874, pp. 37–66 (per Barnard, Roy, 1997, op. Cit., p. 53; “Muster of the Inhabitants in Virginia..” William and Mary College Quarterly Historical Mag., vol 7:4 (April 1899), pp. 217–218 (per Barnard, Roy, 1997, op. Cit., p. 55).
A common surname is no guarantee of relationship. Today genealogists researching Barnard lineages recognize different families descending from the early settlers, and have not fully resolved the relationships, if any, among the early Barnard immigrants.