1- The supplication of seeing the new crescent of Ramadan:
It is to say, “Allahumma ahillahu `alayna bil-amni wal-iman was-salamati wal-islam. Rabbi wa rabbuka Allah (Oh Allah, make it a start full of peace and faith, safety and Islam. My lord and your lord is Allah.)
Notice how this supplication pairs peace and faith as if they are twins. Both words (amn and iman) sound alike because one is derived from the other. In another narration, it mentions (silm “i.e. peace” and Islam) pairing peace and Islam, because again one is derived from the other. In short, the two most important concepts in our religion (Islam and faith) are both derived from the words that mean peace in Arabic, amn and silm. We ask Allah to make this Ramadan full of peace.
2- The supplication of breaking the fast at sunset:
Dhahaba adh-Dhama’ wabtallatil-`urooq wa thabatal-ajr insha’ Allah (Thirst is gone, the veins are wet, and the reward is confirmed, if Allah wills.)
Remember, the time of breaking the fast is one of the times where du‘aa’ is likely to be answered. So, you can accompany this Prophetic du‘aa’ with any other du‘aa’ of your own.
3- The supplication when someone annoys you:
Inniee sa’im, inni saa’im (I’m fasting, I’m fasting)
Imam An-Nawawi mentions that this either should be said loud so the aggressor can hear and hopefully stop, or it should be said in silence as a self-reminder. Yet, the first opinion is stronger.
4- The supplication after breaking fast with a group:
“aftara `indakum as-saa’imoon, wa akala ta`amakum al-abrar, wa sallat `alaikum al-malaa’ikah” (May the fasting people break the fast at your place! And may the pious eat from your food! And may the angels pray for you!)
5- The supplication of the Night of Al-Qadr:
Allahumma innaka `afuwun tuhibbul-` afawa, fa’fu `anni (Oh Allah, You are forgiving, and you love forgiveness, so forgive me!)
Source: muslimmatters.org.Soucre Link