The lists of books claimed not to be cited in the New Testament usually included the following nine books.
1. Judges
2. Ruth
Although not directly quoted the history in these two books is repeatedly mentioned.
3. Ezra
Ezra is not quoted but Nehemiah is. And these two books were one scroll in Hebrew so often considered a single book with a unified structure.
4. Esther
Esther, along with Song of Solomon, is probably the book competing for the least case for being in any way mentioned or alluded to in the New Testament.
5. Ecclesiastes
Ecclesiastes 11:5 is in fact is quoted in Christ’s comment to Nicodemus John 3:8. As this is a comment taking both the breath/wind meanings of pneuma/Ruakh the cite from Ecclesiastes is often missed by English readers.
6. Song of Solomon
7. Lamentations
8. Obadiah
9. Zephaniah
Jonah is sometimes claimed as 10th book, but Jonah 1:17 is cited by Jesus. Like Jonah, Obadiah and Zephaniah are part of the scroll of the Twelve Prophets. Statistically it is not surprising that two of the Twelve would be ‘missed’ in the much shorter New Testament.
Summary
While the lack of quotes for Esther and Song is perhaps noteworthy, nevertheless as part of the Jewish Tanakh all of these nine books are counted by Paul when he says all scripture is useful for teaching, reproof, correction, and training in righteousness (2 Timothy 3:16).