ANSWER:
Raising the finger is an innovation. There is a specific du’a to be recited immediately after the adhan:
It was narrated from Jabir ibn ‘Abd-Allah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) said:
“Whoever says when he hears the call to prayer: ‘Allahumma Rabba hadhihi’l-da’wat il-tammah wa’l-salat il-qaimah, ati Muhammadan il waseelata wa’l-fadeelah, wab’athhu maqaman mahmoodan illadhi wa’adtah (O Allah, Lord of this perfect call and the prayer to be offered, grant Muhammad the privilege (of intercession) and also the eminence, and resurrect him to the praised position that You have promised),’ my intercession for him will be permitted on the Day of Resurrection.”