Here the manuscripts read forefathers, but the 1830 typesetter accidentally shortened it to fathers, probably because of the preceding occurrence of the word father. In the 1840 edition, Joseph Smith restored the reading of the original manuscript—and undoubtedly by reference to that manuscript (since we know he used the original manuscript to make a few corrections in the 1840 edition, especially for the first part of the text). The RLDS text follows the 1840 edition, but the LDS text here follows the 1841 edition, which was set from the 1837 edition.
Both “genealogy of X’s fathers” and “genealogy of X’s forefathers” are found in the Book of Mormon text—and about equally divided: four occurrences of the reading with fathers (1 Nephi 5:14, 1 Nephi 5:16, 1 Nephi 6:1, and Omni 1:18) and three occurrences with forefathers (1 Nephi 3:3, 1 Nephi 19:2, and Alma 37:3).
Summary: Follow in 1 Nephi 19:2 the reading of the original text, “the genealogy of his forefathers”.