When producing the printer’s manuscript, Oliver Cowdery initially wrote “but little” here in Jacob 4:1; then he inserted inline the indefinite article a. There is no change in the level of ink flow, so the correction appears to have been virtually immediate. There seems to be little motivation for Oliver Cowdery to have grammatically edited the text here. Either variant seems acceptable. The fact that the RLDS textual tradition (beginning with the 1858 Wright edition) has continually had the variant “but little” suggests that there doesn’t seem to be anything ungrammatical about “but little” in Jacob 4:1.
Elsewhere the Book of Mormon text has six occurrences of “but little”, but no other occurrence of “but a little”:
But these six examples are all consistently different than the one in Jacob 4:1. In each of these six examples, little either serves as the head of a noun phrase (the first three occurrences and the last one) or is followed by a mass noun (timber, alteration). Only in Jacob 4:1 is little followed by a count noun (words). Moreover, the count noun necessarily occurs in a prepositional phrase (“of my words”) since the sentence “I cannot write but little words” means something different; in such a case, little would have to be replaced by few to maintain the meaning (“I cannot write but few words”).
This difference implies that Jacob 4:1, even without the inserted a, differs considerably from the six other occurrences of “but little” and should therefore be considered a unique expression in the Book of Mormon text.
Summary: Retain in Jacob 4:1 the unique reading “but a little”, the corrected reading in 𝓟.