Pioneer Irish of Onondaga is an early 20th century publication that offers biographies, ancestral pedigrees, and Irish places of origin for immigrants from Ireland who settled in this New York county from about 1776 to 1847. The book is divided into 22 chapters, with 20 of those devoted to various cities, towns, and areas in the county.
In the book it mentions how many of the immigrants arrived in Onondaga having first set foot on the continent in Canada. Therefore, those with Irish ancestors from Canada, upstate New York, and neighboring states, such as Vermont, should also check this book out.
The index at the back of the book is very useful as it contains about 3,200 entries. The vast majority are for names of Irish immigrants who are mentioned, along with a sizeable number of Irish place of origin such as counties, town, and parishes.
As always with such publications that do not cite the source of their information, use it as a guide to help you find the original documents for the person of interest. This book is widely available online via Internet Archive, Familysearch Books, Ancestry, and American Ancestors.