Is there a specific du’aa’ to be recited after each two rak’ahs of Taraaweeh?
Question

Is there a specific du’aa’ to be recited after each two rak’ahs of Taraaweeh?.
Praise be to Allah.Dhikr is a kind of worship, and the basic principle concerning acts of worship is that they are not allowed unless there is evidence to indicate that they are obligatory or mustahabb. It is not permissible to invent a dhikr to be done with an act of worship or before or after it. The Prophet (peace and blessings of Allaah be upon him) prayed qiyaam with his Companions at night, and the Sahaabah prayed qiyaam individually and in congregation, during his lifetime and after his death, and there is no report that they remembered Allaah by reciting a specific du’aa’ after each tasleem. The scholars did not narrate any report of a dhikr recited in unison between each two rak’ahs of taraaweeh by the Sahaabah or those who came after them. This indicates that that did not happen, because the scholars used to narrate that which was more hidden and subtle than this outward, obvious matter. The best of guidance is in following the Prophet (peace and blessings of Allaah be upon him) and following his companions in matters of worship, by doing what they did and avoiding what they avoided. 
But there is nothing wrong with a worshipper supplicating Allaah (du’aa’) or reciting Qur’aan, or remembering his Lord (dhikr), without singling out specific verses or soorahs or dhikrs to be recited between the rak’ahs, and without that being recited in unison, led by an imam or anyone else, because that is not narrated in sharee’ah. The basic principle is to accept what is narrated in sharee’ah concerning acts of worship, how often they are done, how they are done, when they are done, where they are done, the reason why they are done and the way in which they are done. 
Shaykh Muhammad al-‘Abdari ibn al-Haaj said in his book al-Madkhal: Chapter on Dhikr after each two rak'ahs of Taraaweeh prayer: 
He – the imam – should avoid what has been innovated of reciting dhikr after each two rak’ahs of Taraaweeh prayer and raising the voice in that, and reciting it in unison. All of that is bid’ah. It is also forbidden for the muezzin to say after the dhikr following each two rak’ahs of taraaweeh, “Al-salaah yarhamukum Allaah (Prayer, may Allaah have mercy on you),” because this is also an innovation and innovation in religion is forbidden. The best of guidance is the guidance of Muhammad (peace and blessings of Allaah be upon him), then the four caliphs who came after him, then the Sahaabah (may Allaah be pleased with them all), and it is not narrated that any of the salaf did that, and we should be content with what was sufficient for them. 
Al-Madkhal, 2/293, 294. 
For more information please see questions no. 10491 and 21902 
And Allaah knows best.