Question:
Are there any ahadith to prove mentioning Imam Ali (as) in the Adhaan or Eqamah is Mustahab (recommended)?
Answer:
Our jurists are unanimous that the third testimony (Ashhado Anna Aliyan Waliullah) is NOT a part of Azan or Eqama. However, there are narrations both in Shi’a and Sunni books of Hadith confirming that the testimony to the prophecy of the Prophet (p) must be followed by the testimony to the Walayat of Imam Ali. Therefore, some of our renowned scholars have suggested that based on those narrations one may suggest that the third testimony is a recommended part of Azan. The late Allamah al-Majlesi says: “It is possible to claim that the third testimony is one of the recommended parts of Azan, as al-Sheikh (al-Tousi), al-Allamah (al-Hilli), and al-Shahid (al-Awwal) and others have testified that there are narrations about it.” (Behar, vol.81 p.111)
The followings are some of these narrations. The first is a Shi’a source and the other two are from the Sunni books:

1. الشَّيْخُ أَحْمَدُ بْنُ أَبِي طَالِبٍ الطَّبْرِسِيُّ ره فِي كِتَابِ الْإِحْتِجَاجِ عَنِ الْقَاسِمِ بْنِ مُعَاوِيَةَ قَالَ: قُلْتُ لِأَبِي عَبْدِ اللَّهِ ع هَؤُلَاءِ يَرْوُونَ حَدِيثاً فِي مِعْرَاجِهِمْ أَنَّهُ لَمَّا أُسْرِيَ بِرَسُولِ اللَّهِ ص رَأَى عَلَى الْعَرْشِ لَا إِلَهَ إِلَّا اللَّهُ مُحَمَّدٌ رَسُولُ اللَّهِ أَبُو بَكْرٍ الصِّدِّيقُ فَقَالَ سُبْحَانَ اللَّهِ غَيَّرُوا كُلَّ شَيْ‌ءٍ حَتَّى هَذَا قُلْتُ نَعَمْ قَالَ إِنَّ اللَّهَ عَزَّ وَ جَلَّ لَمَّا خَلَقَ الْعَرْشَ كَتَبَ عَلَيْهِ لَا إِلَهَ إِلَّا اللَّهُ مُحَمَّدٌ رَسُولُ اللَّهِ عَلِيٌّ أَمِيرُ الْمُؤْمِنِينَ ثُمَّ ذَكَرَ ع كِتَابَةَ ذَلِكَ عَلَى الْمَاءِ وَ الْكُرْسِيِّ وَ اللَّوْحِ وَ جَبْهَةِ إِسْرَافِيلَ وَ جَنَاحَيْ جَبْرَئِيلَ وَ أَكْنَافِ السَّمَاوَاتِ وَ الْأَرَضِينَ وَ رُءُوسِ الْجِبَالِ وَ الشَّمْسِ وَ الْقَمَرِ ثُمَّ قَالَ ع فَإِذَا قَالَ أَحَدُكُمْ لَا إِلَهَ إِلَّا اللَّهُ مُحَمَّدٌ رَسُولُ اللَّهِ فَلْيَقُلْ عَلِيٌّ أَمِيرُ الْمُؤْمِنِينَ. (الإحتجاج ص 83)

Al-Sheikh al-Tabresi narrated from Qasim Ibn Mo’awiya: I mentioned to Imam al-Sadiq (a.s) that they (i.e. the Sunnis) narrate when the Messenger of Allah (P) was ascended to heaven, he saw on the Throne (written): La Ilaha Ellallah, Muhammad Rasoulullah, AbuBakr al-Siddiq. The Imam said: Glory to Allah, they perverted everything even this? I said, yes. He then said: When the Almighty Allah created the Throne, He wrote on it: La Ilaha Ellallah, Muhammad Rasoulullah, Ali Amirul-Mo’meneen. Then the Imam mentioned that the same was written on the ‘Water’, ‘the Chair’, ‘the Tablet’, ‘the Forehead of Israfil’, and ‘the two Wings of Jabraeil’, and around the heavens and the earth, and the pick of mountains, the Sun and the Moon. The Imam then continued: Thus, when one of you says: La Ilaha Elllallah, Muhammad Rasoolullah, he shall also say: Ali Amirul-Mo’meneen.”

2. ابی الحمراء عن رسول الله (ص) قال: لمّا إسری بی الی السماء اذا علی العرش مکتوب: لا اله الاّ الله، محمد رسول الله ایّدته بعلیّ. (الدر المنثور ج4 ص 153)

Abil-Hamra’ narrated from the Messenger of Allah (p): “when I was ascended to the heaven, I saw on the Throne written ‘La Ilaha Ellallah, Muhammad Rasoulullah, I supported him with Ali.”

3. عن حذيفة عن رسول الله (ص) قال: لو علم الناس متى سمّي علي أمير المؤمنين ما انكروا فضله ، سمّي أمير المؤمنين وآدم بين الروح والجسد ، قال الله تعالى: وإذ أخذ ربّك من بني آدم من ظهورهم ذريّتهم واشهدهم على انفسهم الست بربّكم قالت الملائكة بلى فقال: أنا ربّكم محمد نبيّكم علي أميركم. (فردوس الاخبار ديلمي ج 3 ص 399 )

“Hozayfa narrated from the Messenger of Allah (p): “If people knew when Ali is called Amirul-Mo’meneen they would not have denied his virtues. He was called Amirul-Mo’meneen when Adam was (still) between body and soul (i.e. he was not physically created yet). The Almighty Allah said: ‘when your Lord brought forth from the children of Adam, from their loins, their seed and made them testify as to themselves (saying): Am I not your Lord? They said: yes’ then He said: I am your Lord, Muhammad your prophet, Ali your leader.”