Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
It is not narrated that the Prophet (peace be upon him) or the companions, as far as we know, said any specific duaa or dhikr between the two khutbahs of Jumuah. Rather some of the scholars said that it is recommended to say duaa between the two khutbahs, seeking the time when duaa is answered on Friday.
Almighty Allah knows best.
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