What is the virtue of the Duha prayer and what is the supplication recited after it?

There is no specific, authentic supplication after the Duha prayer. What is mentioned of the supplication, "O Allah, verily the Duha is Your Duha, and the splendor is Your splendor, and the beauty is Your beauty..." has no basis in the Sunnah. It contains weakness, artificiality, and unlawful intercession, so one should not supplicate with it.