Is it permissible to recite the morning and evening adhkar during Fajr and 'Asr prayers, with the exception of the Quranic verses?

There is no impediment to reciting morning and evening remembrances (adhkar) during prayer, especially in positions where general remembrance (dhikr) and supplication (du'a) are legislated, such as prostration (sujud (definition)), after the final tashahhud (definition), and during the witr qunut. This is based on prophetic traditions that encourage supplication in prostration and allow for choice in supplication after the tashahhud. Furthermore, these remembrances do not necessitate any deficiency, and the Lawgiver has permitted absolute remembrance and supplication.