Regarding the Judges judge when he is mistaken

Umm Salamah reported the Messenger of Allah ﷺ as saying:
"I am only a human being, and you bring your disputes to me, some perhaps being more eloquent in their plea than others, so that I give judgement on their behalf according to what I hear from them. Therefore, whatever I decide for anyone which by right belongs to his brother, he must not take anything, for I am granting him only a portion of Hell.

حَدَّثَنَا مُحَمَّدُ بْنُ كَثِيرٍ، أَخْبَرَنَا سُفْيَانُ، عَنْ هِشَامِ بْنِ عُرْوَةَ، عَنْ عُرْوَةَ، عَنْ زَيْنَبَ بِنْتِ أُمِّ سَلَمَةَ، عَنْ أُمِّ سَلَمَةَ، قَالَتْ قَالَ رَسُولُ اللَّهِ ﷺ " إِنَّمَا أَنَا بَشَرٌ وَإِنَّكُمْ تَخْتَصِمُونَ إِلَىَّ وَلَعَلَّ بَعْضَكُمْ أَنْ يَكُونَ أَلْحَنَ بِحُجَّتِهِ مِنْ بَعْضٍ فَأَقْضِيَ لَهُ عَلَى نَحْوِ مَا أَسْمَعُ مِنْهُ فَمَنْ قَضَيْتُ لَهُ مِنْ حَقِّ أَخِيهِ بِشَىْءٍ فَلاَ يَأْخُذْ مِنْهُ شَيْئًا فَإِنَّمَا أَقْطَعُ لَهُ قِطْعَةً مِنَ النَّارِ " .

Umm Salamah said:
Two men came to the Messenger of Allah ﷺ who were disputing over their inheritance. They had no evidence except their claim. The Prophet ﷺ then said in a similar way. Thereupon both the men wept and each of them said: This right of mine go to you. The Prophet ﷺ then said: Now you have done whatever you have done ; do divide it up, aiming at what is right, then drew lots, and let each of you consider the other to have what is legitimately his"

حَدَّثَنَا الرَّبِيعُ بْنُ نَافِعٍ أَبُو تَوْبَةَ، حَدَّثَنَا ابْنُ الْمُبَارَكِ، عَنْ أُسَامَةَ بْنِ زَيْدٍ، عَنْ عَبْدِ اللَّهِ بْنِ رَافِعٍ، مَوْلَى أُمِّ سَلَمَةَ عَنْ أُمِّ سَلَمَةَ، قَالَتْ أَتَى رَسُولَ اللَّهِ ﷺ رَجُلاَنِ يَخْتَصِمَانِ فِي مَوَارِيثَ لَهُمَا لَمْ تَكُنْ لَهُمَا بَيِّنَةٌ إِلاَّ دَعْوَاهُمَا فَقَالَ النَّبِيُّ ﷺ فَذَكَرَ مِثْلَهُ فَبَكَى الرَّجُلاَنِ وَقَالَ كُلُّ وَاحِدٍ مِنْهُمَا حَقِّي لَكَ . فَقَالَ لَهُمَا النَّبِيُّ ﷺ " أَمَّا إِذْ فَعَلْتُمَا مَا فَعَلْتُمَا فَاقْتَسِمَا وَتَوَخَّيَا الْحَقَّ . ثُمَّ اسْتَهِمَا ثُمَّ تَحَالاَّ " .

Umm Salamah reported the Prophet ﷺ as saying when two men were disputing over inheritance and old things:
I decide between you on the basis of my opinion in cases about which no revelation has been sent down to me.

حَدَّثَنَا إِبْرَاهِيمُ بْنُ مُوسَى الرَّازِيُّ، أَخْبَرَنَا عِيسَى، حَدَّثَنَا أُسَامَةُ، عَنْ عَبْدِ اللَّهِ بْنِ رَافِعٍ، قَالَ سَمِعْتُ أُمَّ سَلَمَةَ، عَنِ النَّبِيِّ ﷺ بِهَذَا الْحَدِيثِ قَالَ يَخْتَصِمَانِ فِي مَوَارِيثَ وَأَشْيَاءَ قَدْ دَرَسَتْ فَقَالَ " إِنِّي إِنَّمَا أَقْضِي بَيْنَكُمْ بِرَأْيِي فِيمَا لَمْ يُنْزَلْ عَلَىَّ فِيهِ " .

Narrated Umar ibn al-Khattab:

Umar said while he was (sitting) on the pulpit: O people, the opinion from the Messenger of Allah ﷺ was right, because Allah showed (i.e. inspired) him; but from us it is sheer conjecture and artifice.

حَدَّثَنَا سُلَيْمَانُ بْنُ دَاوُدَ الْمَهْرِيُّ، أَخْبَرَنَا ابْنُ وَهْبٍ، عَنْ يُونُسَ بْنِ يَزِيدَ، عَنِ ابْنِ شِهَابٍ، أَنَّ عُمَرَ بْنَ الْخَطَّابِ، - رضى الله عنه - قَالَ وَهُوَ عَلَى الْمِنْبَرِ يَا أَيُّهَا النَّاسُ إِنَّ الرَّأْىَ إِنَّمَا كَانَ مِنْ رَسُولِ اللَّهِ ﷺ مُصِيبًا لأَنَّ اللَّهَ كَانَ يُرِيهِ وَإِنَّمَا هُوَ مِنَّا الظَّنُّ وَالتَّكَلُّفُ .