This psalm reflects a “two ways” ethic found in Second Temple wisdom literature. Building on the covenant renewal in Deuteronomy 30:11-20, there are only two ways the people can go, either toward life or toward death. If Israel follows the Law, they will be blessed and have peace and material prosperity. However, if they do not follow the Law, they will be cursed and not experience peace and prosperity. Psalm 1 contrasts two kinds of people, the righteous person and the sinner. The righteous is like a tree planted beside water (prosperous and bearing fruit), but the sinner is like a bush growing in the desert, barely surviving and never bearing fruit.
The Psalmist contrasts the righteous (3.3-8) with the sinner (3.9-12). The righteous man has confidence in God and constantly searches his house to remove unintentional sin. He atones for ignorant sin by fasting and humbling his soul.
Psalms of Solomon 3.5-8 The righteous stumbles and proves the Lord right; he falls and watches for what God will do about him; he looks to where his salvation comes from. 6 The confidence of the righteous (comes) from God their savior; sin after sin does not visit the house of the righteous. 7 The righteous constantly searches his house, to remove his unintentional sins. 8 He atones for (sins of) ignorance by fasting and humbling his soul, and the Lord will cleanse every devout person and his house.
In verse 8, the Lord cleanses “every devout person” (ὅσιος). R. B. Wright comments this noun is related to the Hasidim (οἱ Ασιδαῖοι), the righteous ones who supported the Maccabean revolt (1 Macc 2:24, 7:13) but broke with the Hasmoneans and likely developed into the Sadducees, Pharisees and Essenes. Perhaps this is a hint of the origin of the Psalm. Early studies of the Psalms of Solomon identified the author(s) as either Pharisees or Essene and Wright’s introduction in OTP leans that direction.
But Charlesworth adds a paragraph to the introduction warning against labeling the Psalms as either Pharisaic or Essene because so little is known about the Pharisees prior to A.D. 70 (OTP 2:642, see note 8). Since some scholars have claimed the Psalms of Solomon were written by Pharisees, a paragraph like PsSol 3.5-8 is used to develop the views of the Pharisees. But as Charlesworth comments, this is a kind of circular reasoning. Neither Anthony J. J. Saldarini (Pharisees, Scribes and Sadducees in Palestinian Society, Eerdmans 2001) and the collection of essays edited by Jacob Neusner Bruce D. Chilton (In Quest of the Historical Pharisees, Baker, 2007) make little or no reference to the Psalms of Solomon.

The word does not appear in the New Testament, but the cognate ἱλάσκομαι is used in Jesus’s parable of the Pharisee and the tax collector. The tax collector is devastated by his own guilt and cries out to the Lord, “have mercy (ἱλάσκομαι) on me a sinner” (Luke 18:13). In the Parable, the Pharisee boasts in his fasting and careful tithing, but the tax collector “having been made righteous” (a participle from δικαιόω). Someone who had Psalm of Solomon 3:5-8 in mind would have expected the Pharisee to have received mercy since he was carefully examining his life in order to “remove unintentional sins.” Yet Jesus reverses that expectation and the sinner receives mercy and went away from the Temple having been made righteous (δεδικαιωμένος).
Although it is impossible to state dogmatically this Psalm reflects the attitude of the Pharisee in the early first century, it does resonate with the Pharisee of Luke 18.
Once inside the Temple, “They trampled it down (καταπατέω) with their shoes in arrogance” (PsSol 2:2). This description is a possible allusion to 1 Maccabees 3:51, “Your sanctuary is trampled down (καταπατέω) and profaned, and your priests mourn in humiliation” (RSV). In verse 19, the arrogant Gentiles dragged the beauty of the Temple “down from the throne of glory.” According to Josephus, Pompey entered the Temple and “saw all that which it was unlawful for any other men to see, but only for the high priests” (Antiq. 14.4.2).
The usual polemic accusations are made (immorality, breach of purity, theft, etc.) The righteous have suffered, but they have not been destroyed. They are waiting for God’s judgment which will vindicate their suffering, although it may not be in this life. E. P. Sanders considered this as a rather vague belief in an afterlife (Sanders, Judaism, 454). In PsSol. 3:11 “The destruction of the dead is forever and he will not be remembered when God visits the righteous. This is the share of the sinners forever, but those who fear the Lord shall rise up to eternal life and there life shall be in the Lord’s light, and it shall never end.” Notice the righteous will rise to an eternal life of some sort. (John Collins, The Apocalyptic Imagination, 143 also lists 13:11, 14:3, 15:13 and 16:1-3 as implying an afterlife.)
It is difficult to know the goal of this magical text, which is why Charlesworth includes it in his collection of Old Testament Pseudepigrapha despite its presence in Greek Magical Papyri. It does indeed appear to be Jewish. For example, line 17 may allude to Solomon’s request for wisdom: “Fill me with wisdom, empower me, Lord.” God rules over the archangels (line 7) and sits above Sinai (line 8).
Although the prayer originally ran some 1100 lines, only nine are now extant. Since the longest fragment appears in Origin’s Commentary on John, the prayer dates before A.D. 231. Origin introduced the text as “an apocrypha presently in use among the Hebrews.” J. Z. Smith thought the parallels with Hebrew and Aramaic prayers suggest a date in the first century (OTP 2:700). After observing the uncertainty associated with this text, Stephen Robinson suggests the prayer was written in the first century in either in Aramaic or Greek by a Jewish author (ABD 3:976). In his Lexham Bible Dictionary article, John Barry suggests the possibility the text may have “gnostic undertones” since Jacob is described as elevated figure with special abilities and knowledge.