What was Jesus’ favorite book of the Bible? In truth, this would be an impossible question to answer with any measure of certainty. Obviously, we do not have access to Jesus to find out how he would answer. Nor would it be a fair question to ask! It would be akin to asking a parent which child is their favorite.
In addition, it is problematic to select a method for determining a “favorite” book. Does a book that is quoted the most make it the most important? Does that give larger books (like the Psalms) an unfair advantage? What about the polemic nature of some of the quotes? Are not some passages cited because they help Jesus (or Paul or Peter) prove a point? And these are just in reference to actual quotes. What about the hundreds if not thousands of allusions, echoes, and verbal parallels of the Old Testament in the New? All of this makes the answer to the above question highly improbable if not impossible.
Nevertheless, I propose that one of the most prominent Jewish scriptures in the thinking of Jesus as well as the New Testament writers was the book of Deuteronomy.