The surname KERNAGHAN or its Variants appear on the following Sources from Ireland (principally Ulster) from the 17th and 18th Centuries
MUSTER ROLLS (1630) - this was a listing of able-bodied men who were capable of military service. (The term Undertaker in this context is the Landowner)
HEARTH MONEY ROLLS (1660s) - a listing of tax payers levied on the number of Hearths contained in their House. (Note - there is no Listing for County Down).
PROTESTANT HOUSEHOLDERS RETURNS (1740) - all of Londonderry, most of Antrim, part Tyrone and the Barony of Inishowen in Donegal
THE FLAXGROWERS BOUNTY LIST (1796) - a listing of Farmers who, by planting flax on their properties, were granted free spinning wheels by the Irish Linen Board