What is the authenticity of "Salat al-Adhan" or "Sunnat al-Adhan," which consists of two rak'ahs after the Adhan?

The regular Sunnah prayers are twelve rak'ahs: four before Dhuhr and two after it, two after Maghrib, two after Isha, and two before Fajr. Anything other than these is a supererogatory prayer (nafilah). It has been reported that praying between thethan and the iqamah is recommended for whoever wishes to do so, and the Companions used to perform it.