Assalam 'Alaykum,my question is "is there any authentic dua[supplication] after taraweh prayer?.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.

We could not find any specific supplication to be recited after Taraaweeh prayer. However, when the praying person ends his prayer by performing Witr prayer, it is recommended to recite the reported Thikr (mention of Allaah) to be recited after Witr prayer.

An-Nawawi wrote, “It is reported with a Saheeh (sound) Isnaad (chain of narrators) on the authority of Ka‘b ibn Maalik that when the Prophet, sallallaahu ‘alayhi wa sallam, performed Witr prayer, he, sallallaahu ‘alayhi wa sallam, would say: ‘Subhaan Al-Malik Al-Quddoos (which means: Glory be to the Sovereign, the Most Holy).’” [An-Nasaa’i, Abu Daawood, and others] An-Nasaa’i and Ibn As-Sunni cited another version of the Hadeeth stating that he, sallallaahu ‘alayhi wa sallam, used to recite that Thikr thrice.

Moreover, ‘Ali reported that the Prophet, sallallaahu ‘alayhi wa sallam, used to say at the end of the Witr prayer: 'Allaahumma, inni a‘oothu bi-ridhaaka min sakhatik, wa bi mu‘aafatika min ‘uqoobatik, wa bika minka la uhsi thanaa’an ‘alayka anta kama athnayta ‘ala nafsik (O Allaah, I seek refuge in Your pleasure from Your wrath, in Your forgiveness from Your punishment and in You from You. I cannot praise You enough, You are as You have praised Yourself.)’ [An-Nasaa’i, Abu Daawood, and At-Tirmithi; At-Tirmithi: Hasan Saheeh (i.e. good or sound)]” [Al-Athkaar]

Allaah Knows best.