In the printer’s manuscript, Oliver Cowdery originally wrote “and the cities of which had been left desolate”. Later, with heavier ink flow, Oliver crossed out the of. The 1830 edition lacks the of. One possibility is that Oliver removed the of when he proofed 𝓟 against 𝓞. But another possibility is that 𝓞 had of, but since the of is unexpected here the 1830 typesetter omitted it and Oliver later decided to cross out the of in 𝓟. In any event, the correct reading is very likely without any of, even if 𝓞 had it, simply because the Book of Mormon expression is for “X to be desolate”, not for “X to be desolate of ”, as in these other examples referring to places being left desolate:
In the first example, the pronoun it refers to the city of Ammonihah. Here in 3 Nephi 4:1 the extra of initially written in 𝓟 was probably a momentary slip.
David Calabro points out (personal communication) that not every verbal example with desolate is of the simple form “X to be desolate”. There is one example where desolate takes a prepositional complement, namely, in the expression “X to be desolate for Y”, as in “no part of the land was desolate save it were for timber” (Helaman 3:6). In this case, for means something like ‘with respect to’.
Don Brugger suggests (personal communication) another way to explain the original of which in 𝓟: namely, the relative pronoun which in of which could refer to the earlier noun phrase the Nephites rather than to the immediately preceding the cities. This kind of circumlocution for “and the cities of the Nephites which had been left desolate” seems unlikely. The expected expression here in 3 Nephi 4:1 for this proposed interpretation would be simply “and their cities which had been left desolate”, not the convoluted “and the cities of which had been left desolate”.
Summary: Maintain in 3 Nephi 4:1 the 1830 reading and the corrected reading in 𝓟—that is, without the preposition of before which in “and the cities which had been left desolate”.