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Dear Ms. Curry,
Thank you for contacting History Hub!
Based on the information provided, we suggest you look at websites such as FamilySearch and Ancestry to get started for birth, marriage, death, and census records to help piece together a timeline for Andrew J. McFann.
Just a quick search of FamilySearch has let me to a marriage record of Andrew Jackson McFann and Margaret Ann Munyon for 18 Dec 1853 in Scioto County, Ohio (there is a copy of it on FamilySearch which is available for free). We also suggest that you order a copy of his death certificate through the Ohio History Connection which could provide additional information about his life.
Once you have exhausted those resources, we suggest you check out local historical societies for the area in which he lived. They may be able to provide you with additional resources such as probate or land records. FamilySearch has wonderful wiki pages for local areas that identify where to find various types of records and what repositories are in the area such as for Scioto County, OH.
Once you are able to find more information about Andrew J. McFann and his ancestors, then we can better assist you with finding immigration records from Ireland.
Best of luck in your research!