The Dua After the Call to Prayer
اللَّهُمَّ رَبَّ هَٰذِهِ الدَّعْوَةِ التَّامَّةِ، وَالصَّلَاةِ الْقَائِمَةِ، آتِ مُحَمَّدًا الْوَسِيلَةَ وَالْفَضِيلَةَ، وَابْعَثْهُ مَقَامًا مَحْمُودًا الَّذِي وَعَدْتَهُ
Allahumma rabba hadhihid-da'watit-tammah, was-salatil-qa'imah, ati Muhammadanil-wasilata wal-fadilah, wab'ath-hu maqaman mahmudanil-ladhi wa'adtah.
O Allah, Lord of this perfect call and of the prayer about to be established, grant Muhammad the station of nearness and the highest rank, and raise him to the praiseworthy place You have promised him.
What it means
After the call ends, the first thing you ask for is not for yourself but for the Prophet ﷺ. The station being requested is the one from which he will intercede for his ummah, so asking for it is, in the end, asking for everyone.
When and how
Repeat after the muadhdhin word for word, then send blessings upon the Prophet ﷺ, then say this dua once. The time between the adhan and the iqamah is a time when dua is answered, so follow it with what you need.
Its virtue
The Prophet ﷺ said that whoever says this after hearing the call will be granted his intercession on the Day of Resurrection, reported in Sahih al-Bukhari 614.
Source
Al-Bukhari 614sahih