The Jewish Scriptures were compiled over time in the order in which they were known, used, and gained authority. And this progression can be seen through the Old Testament. First, there was "this book of the Law" (Joshua 1.8). Then, a few hundred years later, in the 8th century BC, Isaiah referenced "the Law and the testimony" (Isa 8.20). About a hundred years after that, Zechariah mentions "the Law and the words" that "the Lord of Hosts sent by his Spirit by the hand of the prophets".
So, as early as the 7th century BC, we have the testimony added to by the prophets. Precisely what the testimony was is unclear. But in the Jewish Sciptures, there are two kinds of prophetic collections: the Minor Prophets and the Major Prophets. The Minor Prophets are Joshua, Judges, Samuel (1 and 2), and Kings (1 and 2). The Major Prophets start with Isaiah and go through to Malachi (the last of the Book of the Twelve).
By Jesus' day, the minor and major prophets were known collectivley as the Prophets. And, as we see starting with Isaiah, their authority was equal to that of the Law.
In the course of time, there were added to the Jewish Scriptures other works like the Psalms, Job, Proverbs, Ruth, Song of Songs, Ecclesiastes, Lamentations, Esther, Daniel, Ezra, Nehemiah, and Chronicles (1 and 2). This addition was called simply the Writings.
The reason Jesus doesn't reference them is because the Writings were not established and were not recognized as authoritative. This is why Jesus never uses them to counter an argument with the Jews.
However, he does use the Prophets to counter Jewish argument from the Torah. In Mark 2.23-28, the Pharisees accuse him of letting his disciples violate the Sabbath (Exodus 20.8-11). But Jesus counters with a reference to 1 Samual 21.1-7, presenting a counter-argument to their reasoning from the Ten Commandments. Consequently, even in Jesus' day, the Prophets were considered equal in authority to the Law, but the Writings were not accorded the same legal weight.