Is there a specific supplication to be recited when the preacher sits between the two Friday sermons?

It has been established that the Prophet, peace and blessings be upon him, used to deliver two sermons on Friday, separated by a brief sitting. No specific supplication (du'a) or remembrance (dhikr) has been reported from the Prophet, peace and blessings be upon him, or the noble companions, to be recited between the two sermons. Some scholars hold the view that it is recommended to supplicate between the two sermons, seeking the hour of responsiveness (sa'at al-ijabah), while others believe that raising one's voice in supplication and disturbing those present is not appropriate. As for reciting the Qur'an during this sitting, it is not established from the Prophet, peace and blessings be upon him. In summary, there is no obligatory Sunnah (definition) for this specific moment. Whoever wishes to occupy these moments with supplication, remembrance, or Qur'an recitation may do so, provided they do not disturb others.