Al-Mundhiri records in his book al-Targhib wal-Tarhib:

الترغيب في صلة الرحم وإن قطعت والترهيب من قطعها

Encouragement to keep good relations with family and discouragement of cutting them off.

Source: al-Targhīb wal-Tarhīb 3/226

Abu Huraira reported: The Prophet, peace and blessings be upon him, said:

مَنْ كَانَ يُؤْمِنُ بِاللَّهِ وَالْيَوْمِ الْآخِرِ فَلْيَصِلْ رَحِمَهُ

Whoever believes in Allah and the Last Day, let him uphold his family ties.

Source: Ṣaḥīḥ al-Bukhārī 6138, Grade: Sahih

Anas ibn Malik reported: The Messenger of Allah, peace and blessings be upon him, said,

مَنْ سَرَّهُ أَنْ يُبْسَطَ لَهُ فِي رِزْقِهِ أَوْ يُنْسَأَ لَهُ فِي أَثَرِهِ فَلْيَصِلْ رَحِمَهُ

Whoever is pleased to have his provision expanded and his life span extended, let him keep good relations with his family.

Source: Ṣaḥīḥ al-Bukhārī 2067, Grade: Muttafaqun Alayhi

Abu Huraira reported: The Prophet, peace and blessings be upon him, said:

تَعَلَّمُوا مِنْ أَنْسَابِكُمْ مَا تَصِلُونَ بِهِ أَرْحَامَكُمْ فَإِنَّ صِلَةَ الرَّحِمِ مَحَبَّةٌ فِي الْأَهْلِ مَثْرَاةٌ فِي الْمَالِ مَنْسَأَةٌ فِي الْأَثَرِ

Learn your lineages to solidify your family ties. Verily, keeping family ties causes love among the kinship, enriches the wealth, and increases the lifespan.

Source: Sunan al-Tirmidhī 1979, Grade: Jayyid

Qatadah reported: A man of Khath’am came to the Prophet, peace and blessings be upon him, and he said, “O Messenger of Allah, which deeds are most beloved to Allah?” The Prophet said:

إِيمَانٌ بِاللَّ

Faith in Allah.

The man said, “Then what?” The Prophet said:

صِلَةُ الرَّحِمِ

To maintain family relationships.

The man said, “O Messenger of Allah, which deeds are most hateful to Allah?” The Prophet said:

الإِشْرَاكُ بِاللَّهِ

To associate idols with Allah.

The man said, “Then what?” The Prophet said:

قَطِيعَةُ الرَّحِمِ

To sever family relationships.

The man said, “Then what?” The Prophet said:

الأَمْرُ بِالْمُنْكَرِ وَالنَّهْيِ عَنِ الْمَعْرُوفِ

To enjoin evil and forbid good.

Source: Musnad Abī Ya’lá 6839, Grade: Sahih

Abu Ayyub reported: A man came to the Prophet, peace and blessings be upon him, and he said, “Tell me what I can do to enter Paradise and avoid Hellfire.” The Prophet said:

تَعْبُدُ اللَّهَ لَا تُشْرِكُ بِهِ شَيْئًا وَتُقِيمُ الصَّلَاةَ وَتُؤْتِي الزَّكَاةَ وَتَصِلُ ذَا رَحِمِكَ

Worship Allah and do not associate anything with Him, perform prayer, give in charity, and keep good relations with your family.

When the man turned away, the Prophet said:

إِنْ تَمَسَّكَ بِمَا أُمِرَ بِهِ دَخَلَ الْجَنَّةَ

If he adheres to what he has been commanded, then he will enter Paradise.

Source: Ṣaḥīḥ al-Bukhārī 1396, Grade: Muttafaqun Alayhi

Aisha reported: The Prophet, peace and blessings be upon him, said:

إِنَّهُ مَنْ أُعْطِيَ حَظَّهُ مِنْ الرِّفْقِ فَقَدْ أُعْطِيَ حَظَّهُ مِنْ خَيْرِ الدُّنْيَا وَالْآخِرَةِ وَصِلَةُ الرَّحِمِ وَحُسْنُ الْخُلُقِ وَحُسْنُ الْجِوَارِ يَعْمُرَانِ الدِّيَارَ وَيَزِيدَانِ فِي الْأَعْمَارِ

Verily, whoever has been given the quality of kindness has been given his share of good in this life and in the Hereafter. Maintaining family ties, good character, and good treatment of neighbors will build their heavenly abodes and increase their life spans.

Source: Musnad Aḥmad 25259, Grade: Sahih

Abu Dharr reported:

أَوْصَانِي خَلِيلِي صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ بِخِصَالٍ مِنَ الْخَيْرِ أَوْصَانِي بِأَنْ لَا أَنْظُرَ إِلَى مَنْ هُوَ فَوْقِي وَأَنْ أَنْظُرَ إِلَى مَنْ هُوَ دُونِي وَأَوْصَانِي بِحُبِّ الْمَسَاكِينِ وَالدُّنُوِّ مِنْهُمْ وَأَوْصَانِي أَنْ أَصِلَ رَحِمِي وَإِنْ أَدْبَرَتْ وَأَوْصَانِي أَنْ لَا أَخَافَ فِي اللَّهِ لَوْمَةَ لَائِمٍ وَأَوْصَانِي أَنْ أَقُولَ الْحَقَّ وَإِنْ كَانَ مُرًّا وَأَوْصَانِي أَنْ أُكْثِرَ مِنْ قَوْلِ لَا حَوْلَ وَلَا قُوَّةَ إِلَّا بِاللَّهِ فَإِنَّهَا كَنْزٌ مِنْ كُنُوزِ الْجَنَّةِ

My dear friend, the Prophet, peace and blessings be upon him, instructed me with virtuous traits. He instructed me not to look at those above me and to look at those below me. He instructed me to love the poor and be close to them. He instructed me to maintain my family ties even if they turn their backs. He instructed me not to fear the blame of the blamer in the matter of Allah. He instructed me to speak the truth even if it is bitter. He instructed me to increase in declaring there is no power or might but in Allah, for it is a treasure among the treasures of Paradise.

Source: Ṣaḥīḥ Ibn Ḥibbān 449, Grade: Sahih

Aisha reported: The Messenger of Allah, peace and blessings be upon him, said:

الرَّحِمُ مُعَلَّقَةٌ بِالْعَرْشِ تَقُولُ مَنْ وَصَلَنِي وَصَلَهُ اللَّهُ وَمَنْ قَطَعَنِي قَطَعَهُ اللَّهُ

The bond of family is suspended from the Throne and it says: Whoever upholds me, Allah will uphold him. Whoever severs me, Allah will sever him.

Source: Ṣaḥīḥ al-Bukhārī 5989, Grade: Muttafaqun Alayhi

Abdur Rahman ibn ‘Awf reported: The Prophet, peace and blessings be upon him, said:

قَالَ اللَّهُ أَنَا اللَّهُ وَأَنَا الرَّحْمَنُ خَلَقْتُ الرَّحِمَ وَشَقَقْتُ لَهَا مِنْ اسْمِي فَمَنْ وَصَلَهَا وَصَلْتُهُ وَمَنْ قَطَعَهَا بَتَتُّهُ

Allah said: I am Allah and I am the Merciful. I created the womb and I derived it from My name. Whoever upholds it, I will uphold him. Whoever severs it, I will deprive him of My mercy.

Source: Sunan al-Tirmidhī 1907, Grade: Sahih

Abu Huraira reported: The Messenger of Allah, peace and blessings be upon him, said:

إِنَّ اللَّهَ خَلَقَ الْخَلْقَ حَتَّى إِذَا فَرَغَ مِنْهُمْ قَامَتْ الرَّحِمُ فَقَالَتْ هَذَا مَقَامُ الْعَائِذِ مِنْ الْقَطِيعَةِ قَالَ نَعَمْ أَمَا تَرْضَيْنَ أَنْ أَصِلَ مَنْ وَصَلَكِ وَأَقْطَعَ مَنْ قَطَعَكِ قَالَتْ بَلَى قَالَ فَذَاكِ لَكِ

Verily, Allah made the creation and when He finished, the womb said: In this place, I seek refuge in you from those who sever me. Allah said: Are you not pleased that I keep good relations with those who are good to you and I will cut off whoever severs relations with you? The womb said: Yes, my Lord. Allah said: Thus, you will have it.

Then, the Prophet said:

اقْرَءُوا إِنْ شِئْتُمْ فَهَلْ عَسَيْتُمْ إِنْ تَوَلَّيْتُمْ أَنْ تُفْسِدُوا فِي الْأَرْضِ وَتُقَطِّعُوا أَرْحَامَكُمْ

Recite the verse if you wish: Will you then, if you were given authority, spread corruption in the land and sever your family ties? (47:22)

Source: Ṣaḥīḥ al-Bukhārī 5987, Grade: Muttafaqun Alayhi

Abu Huraira reported: The Prophet, peace and blessings be upon him, said:

إِنَّ الرَّحِمَ شَجْنَةٌ مِنْ الرَّحْمَنِ فَقَالَ اللَّهُ مَنْ وَصَلَكِ وَصَلْتُهُ وَمَنْ قَطَعَكِ قَطَعْتُهُ

Verily, the womb derives its name from the Merciful. Allah said: I will keep good relations with one who keeps good relations with your relatives, and I will sever relations with one who severs relations with your relatives.

Source: Ṣaḥīḥ al-Bukhārī 5988, Grade: Sahih

Anas reported: The Prophet, peace and blessings be upon him, said:

إِنَّ لِلرَّحِمِ حُجْنَةً مُتَمَسِّكَةً بِالْعَرْشِ تَكَّلَّمُ بِلِسَانٍ ذَلِقٍ اللَّهُمَّ صِلْ مَنْ وَصَلَنِي وَاقْطَعْ مَنْ قَطَعَنِي فَيَقُولُ اللَّهُ تَبَارَكَ وَتَعَالَى أَنَا الرَّحْمَنُ الرَّحِيمُ وَإِنِّي شَقَقْتُ الرَّحِمَ مِنَ اسْمِي فَمَنْ وَصَلَهَا وَصَلْتُهُ وَمَنْ بَتَكَهَا بَتَكْتُهُ

Verily, the womb has an iron hook attached firmly to the Throne, speaking with a penetrating tongue: O Allah, keep relations with whoever keeps relations with me, and sever relations with whoever severs them with me. Allah Almighty says: I am the Gracious, the Merciful. I derived the womb from My name. Whoever keeps relations with it, I keep relations with him. Whoever cuts off relations with it, I cut off relations with him.

Source: Musnad al-Bazzār 6495, Grade: Hasan li ghayrihi

Sa’id ibn Zayd reported: The Prophet, peace and blessings be upon him, said:

إِنَّ هَذِهِ الرَّحِمَ شِجْنَةٌ مِنَ الرَّحْمَنِ فَمَنْ قَطَعَهَا حَرَّمَ اللهُ عَلَيْهِ الْجَنَّةَ

Verily, this womb is a branch from the Merciful. Whoever severs relations with it, Allah forbids him from entering Paradise.

Source: Musnad Aḥmad 1651, Grade: Sahih

Abdullah ibn Amr reported: The Prophet, peace and blessings be upon him, said:

لَيْسَ الْوَاصِلُ بِالْمُكَافِئِ وَلَكِنْ الْوَاصِلُ الَّذِي إِذَا قُطِعَتْ رَحِمُهُ وَصَلَهَا

The one who keep good relations with family is not the one who compensated. Rather, the one who keeps good relations with family is one who does so despite being cut off by them.

Source: Ṣaḥīḥ al-Bukhārī 5991, Grade: Sahih

Abu Huraira reported: A man said, “O Messenger of Allah, I have relatives with whom I try to relate but they cut me off. I treat them well, but they treat me badly. I am forbearing with them, but they are harsh with me.” The Prophet, peace and blessings be upon him, said:

لَئِنْ كُنْتَ كَمَا قُلْتَ فَكَأَنَّمَا تُسِفُّهُمُ الْمَلَّ وَلاَ يَزَالُ مَعَكَ مِنَ اللَّهِ ظَهِيرٌ عَلَيْهِمْ مَا دُمْتَ عَلَى ذَلِكَ ‏

If it is as you say, then it is as if you threw hot ashes at them. Allah will be with you as a supporter as long as you remain like so.

Source: Ṣaḥīḥ Muslim 2558, Grade: Sahih

Abu Ayyub reported: The Messenger of Allah, peace and blessings be upon him, said:

إِنَّ أَفْضَلَ الصَّدَقَةِ الصَّدَقَةُ عَلَى ذِي الرَّحِمِ الْكَاشِحِ

Verily, the best act of charity is one given to an estranged relative.

Source: Musnad Aḥmad 23530, Grade: Sahih

Hakim ibn Hizam reported: A man asked the Messenger of Allah, peace and blessings be upon him, “What act of charity is best?” The Prophet said:

عَلَى ذِي الرَّحِمِ الْكَاشِحِ

One given to an estranged relative.

Source: Musnad Aḥmad 15320, Grade: Sahih

‘Uqbah ibn ‘Amr reported: I met the Messenger of Allah, peace and blessings be upon him, and he said to me:

يَا عُقْبَةُ صِلْ مَنْ قَطَعَكَ وَأَعْطِ مَنْ حَرَمَكَ وَاعْفُ عَمَّنْ ظَلَمَكَ

O ‘Uqbah, reconcile with whoever cuts you off, give to whoever deprives you, and forgive whoever wrongs you.

Source: Musnad Aḥmad 17452, Grade: Sahih

In another narration, the Prophet said:

أَلَا وَمَنْ أَرَادَ أَنْ يُمَدَّ لَهُ فِي عُمُرِهِ وَيُوَسَّعَ لَهُ رِزْقُهُ فَلْيَصِلْ ذَا رَحِمٍ مِنْهُ

No doubt, whoever wants to extend his lifespan and expand his provision, let him uphold his family ties.

Source: Shu’ab al-Imān 7587, Grade: Sahih li ghayrihi

Abu Bakrah reported: The Messenger of Allah, peace and blessings be upon him, said:

مَا مِنْ ذَنْبٍ أَجْدَرُ أَنْ يُعَجِّلَ اللَّهُ تَعَالَى لِصَاحِبِهِ الْعُقُوبَةَ فِي الدُّنْيَا مَعَ مَا يَدَّخِرُ لَهُ فِي الآخِرَةِ مِثْلُ الْبَغْىِ وَقَطِيعَةِ الرَّحِمِ

No sin deserves quicker punishment from Allah Almighty for its doer in the world, along with what is prepared for him in the Hereafter, than transgression and severing family ties.

Source: Sunan al-Tirmidhī 2511, Grade: Sahih

Abu Bakrah reported: The Prophet, peace and blessings be upon him, said:

إِنَّ أَعْجَلَ الطَّاعَةِ ثَوَابًا صِلَةُ الرَّحِمِ حَتَّى إِنَّ أَهْلَ الْبَيْتِ لِيَكُونُوا فَجَرَةً فَتَنْمُو أَمْوَالُهُمْ وَيَكْثُرُ عَدَدُهُمْ إِذَا تَوَاصَلُوا وَمَا مِنْ أَهْلِ بَيْتٍ يَتَوَاصَلَونَ فَيَحْتَاجُونَ

Verily, the quickest act of obedience to be rewarded is to maintain family ties, even if the people of the household are wicked, such that it will grow their wealth and increase their numbers if they maintain family ties. No people of a household maintain family ties and remain in need.

Source: Ṣaḥīḥ Ibn Ḥibbān 440, Grade: Sahih

Abu Huraira reported: The Messenger of Allah, peace and blessings be upon him, said:

إِنَّ أَعْمَالَ بَنِي آدَمَ تُعْرَضُ كُلَّ خَمِيسٍ لَيْلَةَ الْجُمُعَةِ فَلَا يُقْبَلُ عَمَلُ قَاطِعِ رَحِمٍ

Verily, the deeds of the children of Adam are presented every Thursday, when night turns into Friday. The deeds are not accepted from one who severed his family ties.

Source: Musnad Aḥmad 10272, Grade: Hasan

Abu Musa reported: The Prophet, peace and blessings be upon him, said:

ثَلَاثَةٌ لَا يَدْخُلُونَ الْجَنَّةَ مُدْمِنُ خَمْرٍ وَقَاطِعُ رَحِمٍ وَمُصَدِّقٌ بِالسِّحْرِ

Three will not enter Paradise: the stubborn drunkard, the one who severs family ties, and the believer in magic.

Source: Musnad Aḥmad 19569, Grade: Sahih li ghayrihi

Jubayr ibn Mut’im reported: The Messenger of Allah, peace and blessings be upon him, said:

لاَ يَدْخُلُ الْجَنَّةَ قَاطِعُ رَحِمٍ ‏

The one who severs his family ties will not enter Paradise.

Source: Ṣaḥīḥ al-Bukhārī 5984, Grade: Muttafaqun Alayhi