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 "1900/01 DISTRIBUTION" from the Menu at the Top).