William Kernaghan - Wm Kernahan

His Father Thomas Kernaghan lived in USA most of his life though didn't he?

I think you are conflating two different men, both named William Kernaghan.

This William was born (1827), married (1850) and died (1902) in NY: https://www.familysearch.org/tree/person/details/9HNQ-BPB

William Kernaghan married Margery Castles in Ireland in 1852, while the American William was having his children in NY.

The 1901 Census of Ireland has the Wm m Margarey Castles as being born in Ireland. It would be unusual for people to be born in the USA and migrate to Ireland in the mid 1800s. I think Alex is right that he has been mixed up with another William.