What is the ruling on praying the "Sunnah of Jumu'ah" before the Jumu'ah prayer? Is it a Sunnah or an innovation? And is it permissible to act upon it?

The Prophet (peace be upon him) and his Companions did not pray after the second Adhan for Jumu'ah. This was mentioned by Shaykh al-Islam Ibn Taymiyyah and Ibn al-Qayyim. The intention behind the Adhan here is the one that occurs when the Imam ascends the minbar, because it was not possible to pray after it. As for the muezzin's statement, "Pray the Sunnah of Jumu'ah, may Allah have mercy on me and on you," it was not known in the early era.

Regarding the first Adhan (which Uthman initiated), the jurists differed: The Hanafis and Shafi'is held that praying before Jumu'ah is recommended, but they differed on the number of rak'ahs. The Malikis disliked voluntary prayers at the time of the first Adhan for those already seated in the mosque, but not before it. The Hanbali madhhab is that there is no regular Sunnah prayer before Jumu'ah, but voluntary prayer (such as praying four rak'ahs) is recommended and permissible.