Initially in the original manuscript, Oliver Cowdery skipped the phrase of Nephi and the first occurrence of the subject pronoun they. Both seem necessary here. Elsewhere, whenever the text has the phrase “of the reign of the judges over the people”, the word people is postmodified by either of Nephi (44 times) or of the Nephites (once, in Helaman 7:1). The they here seems to refer to the people themselves, as is suggested by the second occurrence of they (in verse 2): “nevertheless they did not long maintain an entire peace in the land”. The ink level for the supralinearly inserted phrase of Nephi and the subject pronoun they is somewhat heavier, which suggests that both corrections were made at the same time, probably when Oliver read the text back to Joseph Smith.
It should be noted that in this passage we have an initial sentence fragment that is never completed, but is followed by a new clause beginning with nevertheless. This kind of construction is similar to the use of wherefore following an initial sentence fragment (see the discussion under 1 Nephi 11:1). Wherefore acts positively, like the conjunction and, while nevertheless acts negatively, like the conjunction but.
Summary: Accept in Alma 51:1 the corrected reading in 𝓞, “over the people of Nephi / they having established peace”.