The person who increased the number of Adhans for the Jumua prayers to three was ʿUthman bin ʿAffan and it was when the number of the (Muslim) people of Medina had increased. In the lifetime of the Prophet ﷺ there was only one Mu'adh-dhin and the Adhan used to be pronounced only after the Imam had taken his seat (i.e. on the pulpit).  

أَنَّ الَّذِي زَادَ التَّأْذِينَ الثَّالِثَ يَوْمَ الْجُمُعَةِ عُثْمَانُ بْنُ عَفَّانَ ؓ حِينَ كَثُرَ أَهْلُ الْمَدِينَةِ وَلَمْ يَكُنْ لِلنَّبِيِّ ﷺ مُؤَذِّنٌ غَيْرَ وَاحِدٍ وَكَانَ التَّأْذِينُ يَوْمَ الْجُمُعَةِ حِينَ يَجْلِسُ الإِمَامُ يَعْنِي عَلَى الْمِنْبَرِ  

ʿUthman bin ʿAffan introduced the second Adhan on Fridays when the number of the people in the mosque increased. Previously the Adhan on Fridays used to be pronounced only after the Imam had taken his seat (on the pulpit).  

أَخْبَرَهُ أَنَّ التَّأْذِينَ الثَّانِيَ يَوْمَ الْجُمُعَةِ أَمَرَ بِهِ عُثْمَانُ حِينَ كَثُرَ أَهْلُ الْمَسْجِدِ وَكَانَ التَّأْذِينُ يَوْمَ الْجُمُعَةِ حِينَ يَجْلِسُ الإِمَامُ  

"The third Adhan was ordered by 'Uthman when the number of people in Al-Madinah increased. The Messenger of Allah ﷺ only had one Adhan, and the Adhan on Friday was when the Imam sat down."  

أَخْبَرَهُ قَالَ إِنَّمَا أَمَرَ بِالتَّأْذِينِ الثَّالِثِ عُثْمَانُ حِينَ كَثُرَ أَهْلُ الْمَدِينَةِ وَلَمْ يَكُنْ لِرَسُولِ اللَّهِ ﷺ غَيْرُ مُؤَذِّنٍ وَاحِدٍ وَكَانَ التَّأْذِينُ يَوْمَ الْجُمُعَةِ حِينَ يَجْلِسُ الإِمَامُ  

"The third Adhan was ordered by 'Uthman when the number of people in Al-Madinah increased. The Messenger of Allah ﷺ only had one Adhan, and the Adhan on Friday was when the Imam sat down." (Using translation from Nasāʾī 1393)   

إِنَّمَا أَمَرَ بِالتَّأْذِينِ الثَّالِثِ يَوْمَ الْجُمُعَةِ عُثْمَانُ حِينَ كَثُرَ أَهْلُ الْمَدِينَةِ وَلَمْ يَكُنْ لِرَسُولِ اللهِ ﷺ غَيْرُ مُؤَذِّنٍ وَاحِدٍ وَإِنَّمَا كَانَ الْأَذَانُ يَوْمَ الْجُمُعَةِ حِينَ يَجْلِسُ الْإِمَامُ