Is there a supererogatory prayer between the time of Duha prayer and the time of Dhuhr prayer?

There is no specific prayer between Duha (forenoon) and Dhuhr (noon) prayers. However, one may perform absolute voluntary prayers without specifying a number. It is forbidden to perform voluntary prayers at qa'im al-dhahira (midday), which is a short time before the sun declines from its zenith (approximately ten minutes). This is the time when the Prophet, peace and blessings be upon him, forbade prayer. The prayer of the awwabin (oft-returning to Allah) means delaying the Duha prayer until the heat intensifies.