Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, we would like to thank you for the confidence you place in us and we implore Allah Almighty to help us serve His Cause and render our work for His Sake.
In fact, a true believer never gives up supplicating his Lord and imploring Him for guidance. Almighty Allah teaches us to call upon Him and seek His Forgiveness all the time.
In the Qur’an, Almighty Allah teaches us, “Ask Allah of His bounty. Lo! Allah is ever Knower of all things.” (An-Nisaa’ 4:32)
Also, “And when My servant question you concerning Me, then surely I am nigh. I answer the prayer of the suppliant when he cries unto Me. So let them bear My call and let them trust in Me, in order that they may be led aright.” (Al-Baqarah 2:186)
In his Hadith, the Prophet (peace and blessings be upon him) guided us to the importance of du`a’ saying: “Du`a’ is a weapon of a believer, a pillar of religion and a light of the heavens and the earth.” (Al-Hakim) The Prophet (peace and blessings be upon him) also said, “Would I guide you to what would protect you against your enemies and bring you provision? Supplicate to Allah by day and night, for supplication is the weapon of a believer.” (Abu Ya`la Al-Mawsili)
Responding to the question in point, Dr. Rif`at Fawzi, former professor of Shari`ah at Cairo University, states:
There is no specific du`a’ that is said during the pause between the two parts of the Friday khutbah (sermon). However, some Muslim scholars state that at this blessed time du`a’ is answered.
Thus, you can implore Allah using any supplication. The Prophet (peace and blessings be upon him) stated that there is an hour at which Allah responds to supplications on Friday.
Imam Al-Bukhari reported on the authority of Abu Hurairah (may Allah be pleased with him) that Allah’s Messenger (peace and blessings be upon him) talked about Friday and said, “There is an hour (opportune time) on Friday and if a Muslim gets it while praying and asks something from Allah, then Allah will definitely meet his demand.” And he (the Prophet) pointed out the shortness of that time with his hands. (Al-Bukhari)
Determining the exact time of this hour, Al-Muhib At-Tabari stated that the most correct Hadith regarding the exact time of this hour is the one reported by Muslim and Abu Dawud on the authority of Abu Burda Ibn Abu Musa Al-Ash`ari who said: `Abdullah Ibn `Umar said to me, “Did you hear anything from your father narrating something from the Messenger of Allah (peace and blessings be upon him) about the time on Friday?” I said, “Yes, I heard him narrating from the Messenger of Allah (peace and blessings be upon him) (these words), “It is between the time when the imam sits down and the end of the prayer.’” (Muslim and Abu Dawud)
Allah Almighty knows best.