I see them on the 1857 census for Minnesota (that was taken right before the 1858 statehood of Minnesota), and it seems like Hugh might be in Minnesota with his siblings?From the ages of the others.
name: Hugh Hagerty event: Census event place: Township 106, Range 12, Olmsted, Minnesota gender: Male age: 30 race: birthplace: Ireland estimated birth year: 1827 family number: 126 line number: 23 film number: 944287 digital folder number: 004539669 image number: 00115 Household Gender Age Birthplace William HagertyM 24 Ireland Hugh HagertyM 30 Ireland Margarett HagertyF 25 Ireland Ann HagertyF 20 Ireland Ed HagertyM 2 New York John HagertyM 0 Minnesota
This makes it more likely that Edward was born in New York in 1855 or so. Not 1860. And they are not on the 1860 census in New York.
But maybe there is an earlier census, if Hugh Hagerty came to America in 1848. An 1850 census maybe?