Is there a Sunnah indicating the recitation of Surat Al-Jumu'ah in the Isha prayer on Friday night, and what is the reward for one who does so, and is it permissible if it is not a Sunnah?

It has not been reported that the Prophet, peace and blessings be upon him, regularly recited a specific surah in the ‘Isha’ prayer on the night preceding Friday. Persisting in something that the Messenger, peace and blessings be upon him, did not persist in is contrary to what is best, and it may even reach the level of innovation (bid‘ah) if its sunnah status is believed. Therefore, diversity in recitation is advisable.