For I say to you
That unless your righteousness surpasses that of the scribes and Pharisees
You will not enter the kingdom of heaven
Matthew 5:20

What is the “righteousness” of the scribes and Pharisees? To fully answer this question, let’s first define righteousness.

The English word “righteousness” in Matthew 5:20 is transliterated from the Greek word “dikaiosúnee” (NT:1343) and is defined as:
the character or quality of being righteous (1 Jhn 2:29, 1 Jhn 3:7), upright (Pro 16:17, Pro 21:8) or just (1 Pet 3:18, Rom 5:6-9)
conforming to the revealed will of GOD or living a life according to The WORD (Jhn 4:34, Psa 119:6-12, Pro 19:16)
living a life approved by GOD (Jhn 8:29, Rom 12:2, Eph 5:10, Heb 13:20-21)
devoted to a sinless life from your innermost being (Psa 15:1-5, Psa 19:14, Psa 24:3-4, Psa 104:34, Psa 119:97-104)

Before moving forward, it is important, to pause and fully comprehend that, righteousness can only be attained through our Beloved LORD JESUS CHRIST. Apart from HIM we can do nothing (Jhn 15:5).

The scribes and the Pharisees rejected JESUS CHRIST (Luk 9:20-22, Act 4:1-12), yet considered their lives righteous, because they lived according to The LAW of GOD (Rom 9:31-32, Rom 10:2-3, Rom 10:5). Their righteousness was based on their own understanding and ability to keep/obey The LAWS of GOD. Even Paul, who was a Pharisee (Php 3:5) formerly known by his Hebrew name Saul, believed his righteousness to be blameless (Php 3:6, Php 3:9), though guilty of beating, persecuting, imprisoning and murdering believers (Act 22:19-20, Act 26:10-11, 1 Tim 1:13). When reflecting on the beliefs and behavior of the scribes and Pharisees, it is important to consider the following truth:

For whoever keeps the whole law and yet stumbles in one point
He has become guilty of all
For HE who said, “DO NOT COMMIT ADULTERY,” also said, “DO NOT COMMIT MURDER.”
Now if you do not commit adultery, but do commit murder
You have become a transgressor of The LAW
James 2:10-11

Is there an example of what the righteousness of scribes and Pharisees looked like? Yes there are several, the righteousness of the scribes and Pharisees was:
based on outer appearances (Mat 23:5) and public reputation (Mat 6:1-2, Mat 6:5, Mat 6:7, Mat 6:16), instead of a private life that pleases GOD (Psa 15:2, Psa 51:6, Mat 6:3-4, Mat 6:6, Mat 6:8, Mat 6:17-18).
based on hypocrisy (Mat 23:14), pretending to live a life of holiness (Mat 23:25-28); teaching others to live lives they did not (Mat 23:1-3, Rom 2:17-23)
based on works, they measured their holiness on what they did (Luk 18:12, Mat 7:21-23, 1 Cor 13:1-3↔1 Jhn 4:8)
filled with pride (Mrk 12:38-39, Luk 18:9-11, Isa 65:5)
that which caused anger when exposed (Luk 4:24-30, Luk 6:6-11, Act 7:51-54)
that which deceives the one practicing it (Psa 36:1-2, Jer 17:9), the chief priests and scribes beat and tortured our Beloved LORD JESUS CHRIST all night, and sought HIS murder the next day (Mat 27:1-2, Luk 22:1-2), yet they stayed outside of the praetorium so they wouldn’t defile themselves and be unable to eat the Passover meal (Jhn 18:28)

How does one have righteousness that exceeds that of the scribes and Pharisees? Through faith in CHRIST JESUS (Php 3:9), a sincere desire to know HIM and to know HIS WORD (1 Chr 16:8-12, Psa 25:4-5, 1 Jhn 2:3-6, 1 Jhn 5:20), and obedience to HIS WORD (Psa 119:9-11, Psa 119:33-35, Luk 11:28).

But by HIS doing you are in CHRIST JESUS
WHO became to us wisdom from GOD
And righteousness and sanctification, and redemption
1 Corinthians 1:30