According to 1910 US Federal Census, brother James migrated to the USA in 1862. The whole Heffernan family probably migrated at the same time.
Sources
1880 United States Federal Census, resident of Geddes, Onondaga, New York;
New York, State Census, 1905, resident of Syracuse Ward 10, Onondaga, New York;
1910 United States Federal Census, resident of Syracuse Ward 10, Onondaga, New York, aged 53;
Family knowledge;
Clonoulty parish baptism register, National Library of Ireland - priest incorrectly recorded father's name as Thomas Heffernan, but correctly recorded mother's name as Ellen Corcoran;
1952 death record for son Thomas - Michigan, U.S., Death Records, 1867-1952, File Number 8202 32288 - parents recorded as Patrick Ryan and Catherine Heffernan and birthplace as Syracuse, New York;
New York, U.S., County Marriage Records, marriage of Thomas Ryan of Syracuse, 13 March 1914 - his parents recorded as Patrick A. Ryan and Catherine Heffernan;
New York, Death Index, 1880-1956, Certificate Number 17123, 1926.
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DNA Connections
It may be possible to confirm family relationships with Catherine by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Catherine: