The earliest text (in 𝓞 and 𝓟 as well as in all the early editions) reads “in the second day on the first month”, which the editors for the 1920 LDS edition emended to “on the second day in the first month”, consistent with what we expect in English and also generally consistent with usage elsewhere in the Book of Mormon text. It is quite possible that the original manuscript is in error, that somehow the two prepositions in and on got mixed up early on in the transmission of the text.
On the other hand, there is some evidence in the Book of Mormon text for the use of in for days and on for months. To begin with, there is one other example of “in the Xth day” in the earliest text:
𝓞 is not extant here, but since 𝓟 and the 1830 edition are firsthand copies of 𝓞 here and both read in, most likely 𝓞 also read in. One could argue, though, that this in in 3 Nephi 8:5 was the result of the preceding two occurrences of in: “in the thirty and fourth year in the first month”.
Otherwise, the Book of Mormon has “on the Xth day”, but there are only four examples:
We can view these meager statistics (two versus four) as allowing variation between “on the Xth day” and “in the Xth day” in the Book of Mormon text. Also note that the King James Bible has the same kind of variation, with 54 occurrences of “in the Xth day” and 131 of “on the Xth day” (plus 10 of “upon the Xth day”). For example, Exodus 12:3 reads “in the tenth day of this month”. The critical text will therefore restore the original occurrence of “in the Xth day” in Alma 56:1 (“in the second day”) as well as in 3 Nephi 8:5 (“in the fourth day”).
There is no evidence for “on the Yth month” in the King James Bible, but there is some evidence for its use elsewhere in the Book of Mormon. Later on in this chapter of Alma, we have this example for which on is extant in 𝓞:
The use of of here for on is similar to the momentary change Oliver Cowdery made in Alma 56:1 when he copied the text from 𝓞 into 𝓟; there he initially wrote “in the second day of the first month”, but then virtually immediately he corrected the of to on, the reading in 𝓞 (there is no difference in ink flow for the crossout of the of and the supralinear insertion of the on).
There are no other instances in the Book of Mormon of “on the Yth month”, only six examples of “in the Yth month” and three examples of “of the Yth month”:
There is one other case of on with month which has not been edited to in:
Here we have on rather than in. The original manuscript is not extant for this particular preposition, but both 𝓟 and the 1830 edition read on, which means that 𝓞 most likely also read on since in 3 Nephi both 𝓟 and the 1830 edition are firsthand copies of 𝓞. It could be argued that on is used here because of the frequency of the archaic phrase “on the morrow” in the Book of Mormon (37 times). In fact, everywhere else in the text morrow means ‘on the next day’; only here in 3 Nephi 3:8 does it mean simply ‘next’. The Oxford English Dictionary does not list this generalized meaning for morrow, although it gives morrow day, meaning ‘the next day’, with citations beginning in Middle English. We have various examples on Literature Online of morrow day from Early Modern English up into the 1800s (accidentals here regularized):
According to , there are infrequent examples in current English of morrow month, but apparently only in artificial, archaic-sounding language (such as “Good tide hammer, we’ll see you brightly in morrow month!” and “We shall reminisce come the morrow month”).
More generally, there is the occasional example in earlier English of “on the Yth month”, as in this one from Literature Online (spelling regularized but not punctuation or capitalization):
The critical text will therefore restore the original prepositions in Alma 56:1, Alma 56:42, and 3 Nephi 8:5. Although “in the Xth day” and “on the Yth month” are strange for modern English, the original text seems to have had an occasional example of such usage.
Summary: Restore the preposition in for the phrase “in the Xth day” and the preposition on for the phrase “on the Yth month” wherever they occur in the earliest extant text: in Alma 56:1 (“in the second day on the first month”), in Alma 56:42 (“in the morning of the third day on the seventh month”), and in 3 Nephi 8:5 (“in the fourth day of the month”).