I am not sure if cutting some theological things here if we talk about God's righteousness. But for starters I can only reveal what I have learned. For sure, if you want to know about God's righteousness, then one should read the Bible. Because any scripture about Scripture is to be tested and evaluated. But the Truth is the Bible, the Gospel, itself.

Having said that I see that the Bible mostly talks about self-righteousness and God's righteousness. Wherein of course self-righteousness points to the righteousness of man. And these two are very different. 

At one point I see that God's righteousness in when He condemns people, but also when He gives grace or forgives people. But there is righteousness also as a sort of manifestation that is a 180 degrees turn-away from the righteousness of man.

To really understand what is meant, I have read that self-righteousness is used when man goes his own way, (not God's way), and sins. Meaning that man put his own self-righteousness above God's righteousness. The term self-righteousness is in other words the sinful man. (See also Job 35). 

So self-righteousness is not only a man in a sinful state, but also a sinful man. And it operates outside the righteousness of God, and therefore there are two forms here. 

But there is also the question of the ones that are saved. As outlined, if Satan is your father, then you live in self-righteousness. That means that you have a sense of good and bad. But you do not renounce the bad as you are practicing it yourself. And that where it gets cranky because a lot of people who are not saved, (Satan is their father), do not believe that they are bad. Because they think that if they do what they do, and if there is a God, because most are atheists these days, then they are confident that they go to heaven. In this case Satan may have no interest in investing time in you, because then you are already condemned, and God will send you to hell. This is what Christ says.  (REFERENCE)

If you are saved, you know you are going to heaven. It does not mean that you are righteous all the time. Unfortunately we stay sinners until we die or until we are raptured. But saved-ones have another mechanism at work, because God is our Father, He is The Father. And the Father steps in from time to time when you mess up. But here is also a promise, the devil cannot snatch you from the Father's Hand. But God has numerous ways for keeping you on the path of holiness (this is a time consuming transformation). Sometimes that may mean that He prevents you from sinning the sin you do so many times.

Lets shed a little light on unseen self-righteousness that goes on all the time. I should refer to you the YOUTUBE channel "Living Waters" because the core of what they show, you can read down below.

If you know God, you know the righteousness of God. Because that will be opened up to you when you know God. And it is just one of the good character traits that God has. But most of you do not know God. The only thing you know is that God is love. Well I love gaming, but what love is that? And God says: you shall not love the world. But you love the world, don't you? Then you don't know God, you still need to know God's love. And God is righteous, that means He judges. 

If you are not familiar with God's 10 commandments, then you really should take the time to read them. If you ever even only once you have broken one of these, then you have the death penalty for our Holy God. For God death is not eternally out of existence, but eternally in hell. And that is His judgement. This literally means that all that came from the line of Adam and Eve has the death penalty. We are all going to hell by default. Because from birth we are of are our father the devil. And before you start saying, "yeah, but what if a baby dies"? Then you be rest assured that God is righteous. If you know that a baby cannot really sin, then God knows ever so much more than you. He made us, remember?

The godless are blinded for the righteousness of God because they do not know Him. Even a simple conversation already can contain a lot of sin. Lets get practical here. A women's conversation for example. They love to talk. And a lot of women just want to ventilate everything they been through to the highest detail jumping from subject to subject and from person to person. In itself it seems harmless. But what is being talked about? 

Proverbs 18:2 - "A fool has no delight in understanding, But in expressing his own heart."

A fool according to the Bible can express his own heart in several ways that are sinful. 

• To be mindless, and just poor out what ever is in you, not taking account on who your talking to and who you are talking about (= backtalk).
• To say things without understanding. 
• To say things without even listening.

All of these things are poison in conversations. The fool can stir up evil things that others are drawn into or can cause annoyance with others. 

In foolishness hides a lot of evil, it leads to destruction. Read Proverbs, the iceberg of foolishness is described here. The base-word "fool" is used here 78 times. The fool is exposed here as nowhere else in the Bible.

If you don't want to be a fool, then know God the Almighty who made everything seen and unseen. And repent, so God may save you. Amen.