The virtue of Du`a in the last third of the night lies in the fact that Allah descends to the lowest heaven during this time and invites His servants to supplicate to Him. This period is highly praised in Hadiths, where Allah promises to answer those who call upon Him, forgive those who seek forgiveness, and grant requests to those in need. It is a time of divine mercy and an unparalleled spiritual opportunity.

Conclusion: We do not know of anything in the religious texts to indicate that it is mustahabb to have intercourse with one’s wife on Friday night.

Summary of the answer: The way this phrase is to be pronounced is “wa ta‘aala jadduka” with a fat-hah on the jeem, according to scholarly consensus, and what is referred to is greatness. It is not permissible to pronounce it with a kasrah on the jeem (jidduka), because this is distorting the words of the Messenger, who (blessings and peace of Allah be upon him) pronounced it with a fat-hah and the scholars did not refer to any alternative pronunciation.