Uthman forbade the people from performing Hajj at-Tamattu. Ali (RA) questions Uthman, did you not witness the Prophet doing Tamattu? Uthman responds: Of course.

Reference: Sunan an-Nasa'i 2733

Sunan an-Nasa'i 2733
Sa'eed bin Al-Musayyab said:

"Ali and 'Uthman performed Hajj, and when we were partway there, 'Uthman forbade Tamattu, 'Ali said 'When you see him setting out, set out with him (saying the Talbiyah for 'Umrah). So 'Ali and his companions recited the Talbiyah for 'Umrah, and 'Uthman did not forbid them. 'Ali said: 'Have I not been told that you forbade it?' Ali said to him: 'Did you not hear that the Messenger of Allah did Tamattu? He said: 'Of course

أَخْبَرَنَا عَمْرُو بْنُ عَلِيٍّ، قَالَ حَدَّثَنَا يَحْيَى بْنُ سَعِيدٍ، قَالَ حَدَّثَنَا عَبْدُ الرَّحْمَنِ بْنُ حَرْمَلَةَ، قَالَ سَمِعْتُ سَعِيدَ بْنَ الْمُسَيَّبِ، يَقُولُ حَجَّ عَلِيٌّ وَعُثْمَانُ فَلَمَّا كُنَّا بِبَعْضِ الطَّرِيقِ نَهَى عُثْمَانُ عَنِ التَّمَتُّعِ فَقَالَ عَلِيٌّ إِذَا رَأَيْتُمُوهُ قَدِ ارْتَحَلَ فَارْتَحِلُوا ‏.‏ فَلَبَّى عَلِيٌّ وَأَصْحَابُهُ بِالْعُمْرَةِ فَلَمْ يَنْهَهُمْ عُثْمَانُ فَقَالَ عَلِيٌّ أَلَمْ أُخْبَرْ أَنَّكَ تَنْهَى عَنِ التَّمَتُّعِ قَالَ بَلَى ‏.‏ قَالَ لَهُ عَلِيٌّ أَلَمْ تَسْمَعْ رَسُولَ اللَّهِ صلى الله عليه وسلم تَمَتَّعَ قَالَ بَلَى ‏.
Reference  : Sunan an-Nasa'i 2733
In-book reference  : Book 24, Hadith 115
 
Imran bin Hussain: Abgoration of Hajj at-Tamatu was Uthman's own inclination. It was not prohibited by the Prophet (ﷺ).

Reference: Sahih al-Bukhari 4518

Sahih al-Bukhari 4518
Narrated `Imran bin Husain:

The Verse of Hajj-at-Tamatu was revealed in Allah's Book, so we performed it with Allah's Messenger (ﷺ), and nothing was revealed in Qur'an to make it illegal, nor did the Prophet (ﷺ) prohibit it till he died. But the man (who regarded it illegal) just expressed what his own mind suggested.

حَدَّثَنَا مُسَدَّدٌ، حَدَّثَنَا يَحْيَى، عَنْ عِمْرَانَ أَبِي بَكْرٍ، حَدَّثَنَا أَبُو رَجَاءٍ، عَنْ عِمْرَانَ بْنِ حُصَيْنٍ ـ رضى الله عنهما ـ قَالَ أُنْزِلَتْ آيَةُ الْمُتْعَةِ فِي كِتَابِ اللَّهِ فَفَعَلْنَاهَا مَعَ رَسُولِ اللَّهِ صلى الله عليه وسلم، وَلَمْ يُنْزَلْ قُرْآنٌ يُحَرِّمُهُ، وَلَمْ يَنْهَ عَنْهَا حَتَّى مَاتَ قَالَ رَجُلٌ بِرَأْيِهِ مَا شَاءَ‏.‏
Reference  : Sahih al-Bukhari 4518
In-book reference  : Book 65, Hadith 43
 
Ali (RA): "I will not give up the Sunnah of Rasulullah (ﷺ) for any of the people."

Reference: Sunan an-Nasa'i 2723

Sunan an-Nasa'i 2723
It was narrated that Al-Hakam said:

"I heard 'Ali bin Husain narrating from Marwan, that 'Uthman forbade Mut'ah and joining Hajj and "Umrah. 'Ali said; 'Labbaika bi Hajjatin wa 'Umratin ma'an - Here I am, (O Allah) for Hajj and "Umrah together. 'Uthman said: 'Are you doing this when I have forbidden it?' 'Ali said; 'I will not give up the Summah of the Messenger of Allah for any of the people.'''

أَخْبَرَنَا إِسْحَاقُ بْنُ إِبْرَاهِيمَ، قَالَ أَنْبَأَنَا أَبُو عَامِرٍ، قَالَ حَدَّثَنَا شُعْبَةُ، عَنِ الْحَكَمِ، قَالَ سَمِعْتُ عَلِيَّ بْنَ حُسَيْنٍ، يُحَدِّثُ عَنْ مَرْوَانَ، أَنَّ عُثْمَانَ، نَهَى عَنِ الْمُتْعَةِ، وَأَنْ يَجْمَعَ الرَّجُلُ بَيْنَ الْحَجِّ وَالْعُمْرَةِ فَقَالَ عَلِيٌّ لَبَّيْكَ بِحَجَّةٍ وَعُمْرَةٍ مَعًا ‏.‏ فَقَالَ عُثْمَانُ أَتَفْعَلُهَا وَأَنَا أَنْهَى عَنْهَا فَقَالَ عَلِيٌّ لَمْ أَكُنْ لأَدَعَ سُنَّةَ رَسُولِ اللَّهِ صلى الله عليه وسلم لأَحَدٍ مِنَ النَّاسِ ‏.‏
Reference  : Sunan an-Nasa'i 2723
In-book reference  : Book 24, Hadith 105
 
In a different narration, Uthamn claims that it was only performed by Rasulullah (ﷺ) because they were in a state of fear.

Reference: Musnad Ahmad 432

Musnad Ahmad 432
It was narrated that Qatadah said: `Abdullah bin Shaqeeq said:

`Uthman used to forbid mut’ah (of Hajj, i.e., tamattu`) and ‘Ali used to enjoin it. `Uthman said something to `Ali, then `Ali said: You know that we did tamattu` with the Messenger of Allah (ﷺ) . He said: Yes, but we were in a state of fear then.

حَدَّثَنَا مُحَمَّدُ بْنُ جَعْفَرٍ، حَدَّثَنَا شُعْبَةُ، عَنْ قَتَادَةَ، قَالَ قَالَ عَبْدُ اللَّهِ بْنُ شَقِيقٍ كَانَ عُثْمَانُ رَضِيَ اللَّهُ عَنْهُ يَنْهَى عَنْ الْمُتْعَةِ وَعَلِيٌّ رَضِيَ اللَّهُ عَنْهُ يَأْمُرُ بِهَا فَقَالَ عُثْمَانُ رَضِيَ اللَّهُ عَنْهُ لِعَلِيٍّ قَوْلًا ثُمَّ قَالَ عَلِيٌّ رَضِيَ اللَّهُ عَنْهُ لَقَدْ عَلِمْتَ أَنَّا قَدْ تَمَتَّعْنَا مَعَ رَسُولِ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ قَالَ أَجَلْ وَلَكِنَّا كُنَّا خَائِفِينَ‏.
Reference  : Musnad Ahmad 432
In-book reference  : Book 4, Hadith 30

Note: It continued to be practiced during the time of Abu Bakr and Umar and was only abrogated by Uthman.