Michael Patrick McMahon, son of Bernard and Annie (Shields) McMahon, is said to have died 14 November 1975 in Rockaway NJ
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for 1880 you have 2 choices in Jersey City. I favor the first since the second is a carpenter and you'd think he would stay with that trade.
1880, Jersey City
Bernard, 21, working in a tobacco factory
brothers: Michael 24, Thomas 27, Daniel 30, Patrick 18
https://www.familysearch.org/ark:/61903/1:1:MN84-ZGYor
Bernard 22, single, carpenter
brothers: Michael 35, Thomas 27, George 20
mother: Mary, 73, widowed
https://www.familysearch.org/ark:/61903/1:1:MN84-D4T-----------
This might be the other Bernard McMahon, dying July 1881 at age 21-22
https://www.findagrave.com/memorial/146532360/bernard-j.-mcmahon-----------
1900 Weehawken, Bernard McMahon and Bridget
at 1907 Boulevard Loop
Bernard: arrived 1878, naturalized, occ: liquor dealer
https://www.familysearch.org/ark:/61903/1:1:M9JL-41P1910 in Hoboken NJ
Bernard: yardman, coal yard, arrived 1874, naturalized
https://www.familysearch.org/ark:/61903/1:1:MKY8-VR9----------
this might be him, if they were buried in Jersey City:
plot K K 28, Holy Name Cemetery
Bernard McMahon d Nov 1917, age 55
https://www.findagrave.com/memorial/146532355/bernard-mcmahonBridget McMahon d Jun 1915, age 45
https://www.findagrave.com/memorial/146532365/bridget-mcmahon----------
note there are 426 (!) people named McMahon buried in Holy Name Cemetery, Jersey City. So that is what you are up against with this family. I'm not sure any of the records are the man you are looking for, but they do all fit what you know about him.
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looked in vain for Katherine McMahon, b Sep 1883, England, who is with Bernard and Bridget in 1900. She would be the daughter of Bernard and a 1st wife who must have died somewhere before he married Annie Shields. Katherine's immigration information in 1900 said she arrived in 1886.
---> Wait a minute. Bernard might be
neither of those men in Jersey City in 1880 if Katherine is his daughter and was born in England in 1883.
Something doesn't fit about the 1900 census. Bernard says he arrived in the US in 1878, but Katherine was born in 1883. Maybe it is Katherine who doesn't fit with everything else, not the 1880 info for Bernard.
