1) During the time of the Prophet (saw), Abu Bakr and ‘Umar, there was only one Adhān for the Jumu’ah prayer. [Refer to Sahīh Al-Bukhārī 2/393 and Al-Umm of Imām Ash-Shāfi’ī 1/224]
2) During the time of ‘Uthmān, he ordered a prior Adhān to be said in the middle of the market, not inside the masjid. Hence the Sunnah of ‘Uthmān was to call it in the market so that it could serve a benefit. [As stated by Ash-Shātibī and others. Refer to Al-I’tisām 2/146 and Al-Ajwiban Nāfi’ah p.14]
3) He done this due to the increase in the number of Muslims and the expansion of the city dwellers to the furthest point of the city. [Narrated by Abd Ibn Humayd, Ibn Al-Munthir, and Ibn Marduyūh. Refer to Umdat Al-Qārī 3/233, Tabarānī, Tafsīr Al-Qurtubī 18/100, Fath Al-Bāri 2/395 and Tahmīd of Ibn ‘Abdil Barr 10/247]
4) The reasons which prompted ‘Uthmān to do this are no longer present as loud speakers cause people to easily hear the Adhān and there is not one mosque which all the people from the outskirts of the city attend.
5) Accordingly, the prior Adhān has no practical benefit now so one should return to the original state of affairs which the Prophet (saw) and the first two Caliphs were upon.
6) Due to the non-practical benefit of this method, ‘Ali Ibn Abī Tālib went back to the original state and cancelled out this prior Adhān during his Caliphate. [Tafsīr Al-Qurtubī 18/100]
In conclusion, those who still claim to follow ‘Uthmān should follow him as he done the deed and do the prior Adhān in the middle of the market so it can be of benefit. As the reasons no longer hold weight, one should return to the Sunnah of the Prophet (saw) as ‘Alī Ibn Abī Tālib done.