It's one of the books that _____ to me.
We cant say it appeal,because it goes with s,es,ies
this is easy
Only one book appeal to me, among others. So appeal is correct.
There are two cases.
"It's one ... that appeals to me" treating the genitive "of the books" as unnecessary. Correct.
"It's one -of the books that appeal to me-." This way treats the whole rest of the sentence after "one" as a big genitive. Correct. (genitive is the possessive/"of" case)
It could go either way.
I'd say 'It's one of the [group of] books that appeal to me'.
However, for single, 'It's one book that appeals to me.'
"One" is the key word and it's SINGULAR, so the verb that follows MUST be in 3rd person singular:)