Is it impermissible to perform a supererogatory prayer after the Adhan of Asr or after the Asr prayer?

The prohibition of supererogatory prayers (nawafil) after Asr prayer takes effect after performing the Asr prayer, not after the Asr adhan. Whoever has prayed Asr is not permitted to perform supererogatory prayers thereafter until Maghrib, unless these supererogatory prayers are "with a reason" (dhawat asbab), in which case it is permissible according to the most authoritative opinions of the scholars.