What is the Sunnah after the Friday Prayer?

Question :

How did the Messenger of Allah and his Companions, may Allah be pleased with them, used to end the Friday prayer? (I say:) Did the Messenger of Allah pray two Rak'ahs after it, or not? (What is the ruling on performing supererogatory prayers after it?)

Answer:

A similar question to this was previously submitted to the Permanent Committee and it was answered by the following Fatwa:

It has been authentically reported from the Messenger of Allah in the Hadith of Abu Hurairah, may Allah be pleased with him, that he said: "The Messenger of Allah said:

If any of you performs the Friday prayer, then he should offer four Rak'ahs after it.

It is reported on the authority of Ibn 'Umar, may Allah be pleased with him, that: "The Prophet did not pray after the Friday prayer until he had left, then he would offer two Rak'ahs in his house."

The Hadith which proves the legality of praying four Rak'ahs and the Hadith which proves the legality of praying two Rak'ahs are reconciled by saying that one who prays in the mosque should offer four Rak'ahs, while one who prays in his house should offer two Rak'ahs. There is another way of reconciling these two Hadiths, which is to say that the minimum regular Sunnah following the Friday prayer is two Rak'ahs and the maximum is four, whether they are performed in the house or in the mosque.

Source:
The Permanent Committee
Fatawa Islamiyah, Vol. 2 Pages457-458