Is it permissible to recite the adhan supplication after the iqamah?

There is no information reported from the Prophet (peace be upon him) regarding the recitation of the adhan supplication after the iqamah. Therefore, it is not considered appropriate to engage in such a supplication after the iqamah. (Tahtawi, Hashiyah, 190) However, the phrases of the iqamah may be repeated just like the adhan until the prayer begins, or other supplications may be made during the iqamah before the imam starts the prayer. (Ibn Nujaym, al-Bahr, 1/273; al-Fatawa al-Hindiyya, 1/57)

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu