The town is Geneseo in Livingston County, NY. NYS formally starting keeping vital records in 1881. Try looking at the NYS census for 1850 on to get all the people living in a household. Try contacting historical societies, larger public libraries, etc. in the Geneseo area. There might be some church records available. You could look at the NYS 1855 census as this may have information the federal 1850 one does not.