Christ and canon of Old Testament
Some may argue that during Christ’ time on earth, the Jews already had their canon of Scripture (in this case that of Old Testament). New Testament does refer Old testament as “all Scripture” (cf. Luke 24:27, 2 Timothy 3:16). Does this indicate that canon of Old Testament was already fixed before New Testament was written? However, the title “Scripture” can be applied to a book or books long before canon was closed. For example Daniel in the first year of Darius reign already cited Jeremiah (Daniel 9:2) as word of God or as Scripture before Zechariah (Zechariah 1:1) and Haggai (Haggai 1:1) who received revelation in the second year of Darius reign wrote their books.
The present Jewish Scripture has three divisions: Law, Prophets and Writings. Among these three divisions, only two appear in New Testament: Law (of Moses) and Prophets (cf. Matthew 7:12, John 1:45, Acts 13:15, Romans 3:21). The closest we can get to the three divisions is in Luke 24:44 that say “the Law of Moses, the Prophets and Psalms”. However stating that Psalms represents the whole and the rest of the Writings is a weak argument because the same is never applied to the Law and the Prophets. Whilst it indicates the existence of the three divisions of the Jewish scripture, Luke 24:44 gives more evidence that the third division (Writings) in Jesus time was still open-ended. The absence of quotation in New Testament from Esther, Song of Songs, Ecclesiastes, Ezra and Nehemiah, all belong to the Writings, gives further evidence (New Testament does not quote from Obadiah, Nahum and Haggai but the Twelve Minor Prophets was traditionally reckoned as one book. Apparently there is no quotation from Judges, but Ruth, the source of Jesus genealogy in the first Gospel, was commonly combined with it. Also Lamentations, from where there is also no quotation, was commonly combined with Jeremiah).
In New Testament what comprises “Law and Prophets” has loose limit. For example Psalms (in John 10:34) and Isaiah (in 1 Corinthians 14:21) are considered as part of Law. In fact ” Law and the Prophets” might also refer to collection of books of the Old Testament without the third division as attested in 2 Maccabee 15:9. In apocryphal 4 Maccabees 18:10-19 (written in c 50 BC – 50 AD) a series of quotations from “Law and Prophets” include not only those from Genesis, Numbers, Deuteronomy, Isaiah, Ezekiel but also from Daniel, Proverbs and Psalms. We also have testimony from Hegesippus (c. 110 to 180 AD), a Greek Christian, who wrote five books of Hypomnemata or Memoirs. In those books he recorded what he observed on his journey from Corinth to Rome, visiting many churches on the way. Only few fragments are preserved in Eusebius’ (c. 260 to 339 AD) Church History. Hegesippus referred Old and New Testaments as “the Law, the Prophets and the Lord (English Translation from The Nicene and Post-Nicene Fathers, Series II, Vol. 1)
In every succession, and in every city that is held which is preached by the law and the prophets and the Lord.
Eusebius: Church History 4.22.3
Coming back to Luke 24:44, if Christ did refer to the three-fold division of Jewish Scripture then why He did not refer to Daniel, a book that belongs to the third division (refer to Table 1) and has prophecy about Him (Daniel 7:13-14 quoted in Matthew 24:30, 26:64)? It is possible that Christ considered Daniel to belong to the Prophets (as in Septuagint or LXX). Other possible reason why He singled out Psalms in Luke 24:44 is because it has the most numerous reference to Him compared to other books.