Is the correct version this:
But in general such verses have rarely been accepted as a genuine part of the book.
But in general such verses have rarely been accepted as genuine parts of the book.
I (native BrE speaker) think that both sentences are correct but that they express slightly different ideas.
The former sentence, including the phrase "as a genuine part", suggests that the verses referred to form, or rather don't form, one part of the book. I suppose one might think that the whole of chapter X of (name a work of your choice) is made up of the doubtful verses.
In the latter sentence, including the phrase "as genuine parts", suggests that the doubtful verses pop up in various locations throughout a work, some in chapter X, some more in chapter XII, some in chapter XVIII, and so on.
I think this is a very good question, and only one does make sense. Although both might sound fairly acceptable, the second example is grammatically correct. The reason for this is because in the first example, it is using the noun "verses" - which is plural- and describing it as "a part" rather than sticking to using plural vocabulary since the verb "verses" is plural. Therefore, the second example - by using "genuine parts" since it's plural - is grammatically correct.
I hope this response helped!