As explained under Alma 45:13, the expected phrase in the Book of Mormon is “the people of Nephi”, yet “the people of the Nephites” also occurs (although much less frequently). Here in Helaman 7:1, Oliver Cowdery started to write “the people of Nephi” in 𝓟, but he ran out of ink as he was writing Nephi. Having completed only Neph, he redipped his quill and overwrote the ph with pit, and then he continued inline with the final es (thus accidentally omitting the h in his correction). Finally, Oliver inserted the necessary the. Although the original manuscript is not extant for this part of the text, it probably read as “the people of the Nephites” (especially since it is unlikely that Oliver would have emended the text to the less common phraseology). See under Helaman 3:22–23 for another example of this same kind of error by Oliver Cowdery as he copied from 𝓞 into 𝓟.
Summary: Accept in Helaman 7:1 Oliver Cowdery’s corrected reading in 𝓟, “the people of the Nephites”, not the more common “the people of Nephi” (which is what Oliver started to write in 𝓟).