In my Review of the Censuses from the turn of the 20th Century* - 1901 for IRELAND, ENGLAND, SCOTLAND AND CANADA, and 1900 for the UNITED STATES, I came across 35 Surname Variants of KERNAGHAN and these are listed below. (Note: the Documentation for the respective 1901 Censuses of AUSTRALIA and NEW ZEALAND were destroyed upon analysis completion).
Displayed on the Page " CENSUS DISTRIBUTION" are 2 TABLES (with some brief Observations), each Table recording SURNAME VARIANT Distributions, as follows:
1901 BRITISH ISLES by Country (IRELAND, SCOTLAND and ENGLAND)
1901 CANADA and 1900 USA
(These can be accessed by clicking "CENSUS DISTRIBUTION" from the Menu at the foot of this Page).