There is a Killian family in Albany NY that might be worth looking at.
A James Killian died there Feb 25, 1905, son of Edward K and Marcella Farrell (the transcriptions of her name are wrong)
His obit came from
https://www.fultonhistory.com. here is the exact link:
https://www.rootschat.com/links/01prc/text of obit:
Albany NY Argus, February 27, 1905, page 3
Killian-February 25, 1905, James, son of Edward and the late Marcella. Relatives and friends of the family, and those of his brother Patrick F Killian, and uncles Michael Murray and Patrick Killian, are respectfully invited to attend his funeral Monday afternoon at 2 o'clock from his late residence, 49 Lawrence Street. Troy papers please copy.
His brother Patrick F is mentioned in a tree at ancestry,
https://www.rootschat.com/links/01prd/. He was a mason by trade, born about 1869. The tree says he was baptized 3 Nov 1869 in Kilkenny West, Westmeath. The image says his mother's maiden name was Marcella Farrell.
I never saw the name Marcella on an Irish record before, so maybe the tree owner found the right record. However, Kilkenny West is a bit of a ride from Mullingar, so they might not be close relatives.
Patrick F would be too young to be the Patrick you are looking for, but the obit also mentions an uncle Patrick Killian. - Unfortunately, I didn't find him. Edward and Marcella Killian are living with a couple, Michael and Mary Murray, in 1870, so that is probably the other uncle mentioned in Edward's obituary. Mary Murray was born about 1842, too young for the Mary who was the sister of your ancestor, Bridget.
(The more I type this family up, the less I think it is connected to you, but if you look around in Albany and Troy NY you might turn up some more clues.)
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I asked earlier if Patrick might have gone out as a servant. These two Patrick Killian's are in their teens but working for American families. I didn't find them later and haven't eliminated them.
in Saratoga County, NY
1850
https://www.familysearch.org/ark:/61903/1:1:MC1V-HKBin Columbia County, NY
1855
https://www.familysearch.org/ark:/61903/1:1:K6SK-2KS----
But If the Mary and James Killian on Griffith's (on your Westmeath thread) are your family, I doubt Patrick went as a servant. Mary was renting 200 acres+ and James another 60 or so. By comparison, my family had 16 acres, and that was twice what most of the other families in their townland had.
