Dua on Exiting the Masjid
اللَّهُمَّ إِنِّي أَسْأَلُكَ مِنْ فَضْلِكَ
Allaahumma inni as-aluka min-fadlika
O Allah, I ask you of Your favour.
(Muslim)
Source: Central Mosque
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It is sunnah to enter the Musjid with the righjt foot and leave with the left foot. This is established in the Hadith. Hadhrat Anas (Radhiallahu Anhu) reports: “It is from the sunnah (established from the words of Rasulullah (sallallahu alaihi wasallam)) that when you enter the Musjid you should enter with your right foot; and when you leave the Musjid, you should leave with your left foot.”

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Hazrat Fatima (R.A) reported that: when Allah’s Messenger (Peace Be Upon Him) entered the Masjid, he invoked blessings and peace upon Muhammad (himself) and then said: O My Lord, forgive my sins and open unto me the gates of Your Mercy. And as he went out of the Masjid, he would supplicate for blessings and peace upon Muhammad (himself) and say: O My Lord, forgive my sins and open unto me the doors of Your Bounty.
[Muslim, Mishkaat, Chapter: of Masjid and the places of Salah]