What to do in the 3rd and the 4th? A Distinctive Position of ʿAlī b. Abī Ṭālib in Ṣalāt

A distinctive legal position attributed to ʿAlī b. Abī Ṭālib is that he used not to recite any Qur'an (even al-Ḥamd) in the 3rd and 4th unit of prayer.

ʿAbd al-Razzāq al-Ṣanʿānī (d. 211) narrates in his Muṣannaf from Sufyān al-Thawrī from Abū Isḥāq al-Sabīʿī from al-Ḥārith al-Aʿwar that “ʿAlī used not to recite (any Qur’an) in the last two (units) and would call them subḥatayn.“
عبد الرزاق، عَنِ الثَّوْرِيِّ، عَنْ أَبِي إِسْحَاقَ، عَنِ الْحَارِثِ، عَنْ عَلِيٍّ قَالَ: كَانَ لَا يَقْرَأُ فِي الْآخِرَتَيْنِ، وَيُسَمِّيهِمَا سُبْحَتَيْنِ

In another report, ʿAbd al-Razzāq narrates from Maʿmar b. Rāshid from al-Zuhrī from ʿUbaydallāh b. Abī Rāfiʿ (a mawlā who was ʿAlī's scribe) that he (i.e. ʿAlī) used to “Recite Umm al-Qur’an (i.e. al-Ḥamd) and another sūra in the first two units of Ẓuhr and ʻAṣr and would not recite (any Qur’an) in the last two.”
عبد الرزاق، عَنْ مَعْمَرٍ، عَنِ الزُّهْرِيِّ، عَنْ عُبَيْدِ اللَّهِ بْنِ أَبِي رَافِعٍ، قَالَ: كَانَ يَعْنِي: عَلِيًّا - يَقْرَأُ فِي الْأُولَيَيْنِ مِنَ الظُّهْرِ وَالْعَصْرِ بِأُمِّ الْقُرْآنِ وَسُورَةٍ، وَلَا يَقْرَأُ فِي الْآخِرَتَيْنِ

Ibn Abī Shayba (d. 235) has a chapter in his Muṣannaf entitled: man kāna yaqūlu yusabbiḥu fī al-ukharayayni wa lā yuqraʼu or “Those (authorities) who used to assert that one glorifies in the last two (units) and does not recite”. Ibn Abī Shayba can only cite ʿAlī and (arguably) Ibn Masʿūd as companions who held this position.

All the Sunnī madhhabs (with the exception of the Ḥanafīs) ignore ʿAlī's position in favour of reports attributed to other companions which have them reciting al-Ḥamd in the 3rd and the 4th units.

The Imāmī school, on the other hand, and since it authentically preserves the legal positions of al-Bāqir (d. 114) and al-Ṣādiq (d. 148), and since both Imams give preference to the positions of their ancestor ʻAlī in all matters, it comes as no surprise that it allows for one to make tasbīḥ in the last two units.

Thus we find al-Bāqir teaching Zurāra that it is sufficient to say subḥānallāh wa-l-ḥamdulillāh wa lā ilāha illā-llāh wa-llāhu akbar in the last two units.
مُحَمَّدُ بْنُ إِسْمَاعِيلَ، عَنِ الْفَضْلِ بْنِ شَاذَانَ، عَنْ حَمَّادِ بْنِ عِيسى، عَنْ حَرِيزٍ، عَنْ زُرَارَةَ، قَالَ: قُلْتُ لِأَبِي جَعْفَرٍ عليه ‌السلام: مَا يُجْزِئُ مِنَ الْقَوْلِ فِي الرَّكْعَتَيْنِ الْأَخِيرَتَيْنِ؟ قَالَ: أَنْ تَقُولَ: سُبْحَانَ اللهِ، وَالْحَمْدُ لِلّهِ، وَلَا إِلهَ إِلاَّ اللهُ، وَاللهُ أَكْبَرُ، وَتُكَبِّرُ، وَتَرْكَعُ

In another report, al-Bāqir tells Zurāra: “Do not recite anything (of the Qur’an) in the last two units of a four-unit obligatory prayer, whether you are the Imam (leading others) or otherwise.“
Al-Bāqir instructs him to recite subḥānallāh wa-l-ḥamdulillāh wa lā ilāha illā-llāh 3 times instead.
وَرَوَى زُرَارَةُ عَنْ أَبِي جَعْفَرٍ ع أَنَّهُ قَالَ: لَا تَقْرَأَنَ‌ فِي الرَّكْعَتَيْنِ الْأَخِيرَتَيْنِ مِنَ الْأَرْبَعِ الرَّكَعَاتِ الْمَفْرُوضَاتِ شَيْئاً إِمَاماً كُنْتَ أَوْ غَيْرَ إِمَامٍ قَالَ: قُلْتُ: فَمَا أَقُولُ فِيهَا؟ قَالَ: إِنْ كُنْتَ إِمَاماً أَوْ وَحْدَكَ فَقُلْ سُبْحَانَ اللَّهِ وَالْحَمْدُ لِلَّهِ وَلَا إِلَهَ إِلَّا اللَّهُ ثَلَاثَ مَرَّاتٍ تُكَمِّلُهُ تِسْعَ تَسْبِيحَاتٍ ثُمَّ تُكَبِّرُ وَتَرْكَعُ

This is what most Shias practise today and it is something that can be traced back to ʿAlī!