[zatronanec]

Recite the following dikr throughout Ramadan after every fardh Salah.
Ashhadu allahilaha illallah asthagfirullah as-alukal jannatha audhubka minannaar (3times)أشهد أن لا اله إلا الله استغفرالله أسألك ألجنة واعوذ بك من النار
(I bear witness that there is no God but Allah, O Allah forgive me, give me Paradise, protect me from HellFire)




Recite the following dikr after every obligatory salat for the 1st 10days of ramadan. (Make Dua for Mercy)
Allahumma arhamni Ya Arham-mar-Rahimeen (3times)
اللهم ارحمني يا ارحم الراحمين
(Oh Allah have mercy upon me, O Most Merciful)



The following are the dikr to be said after each obligatory salaat for the 2nd third of Ramadan. (Make Dua for forgiveness)
Allahummaghfirli zunubi ya rabbal alameen(3times)
اللهم اغفر لي ذنوبي يا رب العالمين
(O Allah forgive my sins, O Lord of the worlds)





Recite the following 3 times after every prayer for the last 10 days of Ramadan. Also it can be recited anytime for the last 10 days. The last ten days is the time to ask for protection from Hell-fire.
Allahumma innaka `afuwwun tuhibbul'afwa fa'fu'annee
اللهم إنك عفو تحب العفو فاعفو عنا
(O Allah! Verily, You are the Oft-Pardoning, You love to pardon, so pardon me)."

Allahumma ajirnaa min an-Naar
اللهم أجرنا من النار
(O Allah save us from the Fire)



Edit: The explaination from the mod,

Actually, they are established from Hadith. There's a famous Hadith in which 4 things to be done in great abundance in Ramadhan, "two which please Allah and two which you cannot do without"

Two which please: 1. read kalimah 2. seek forgiveness from Allah

Two which you can't do without: 3. ask Allah for entry into Jannah 4. seek protection from Allah

So the first one above is basically the most simple formula of the above 4.

The next three du'as are based on the hadith of the three 'ashara in Ramadhan - first 10 days of Rahma, second ten of Maghfirah and third ten of salvation ('itq min an-naar)... so they are just asking Allah for Mercy in first 10 days, for forgiveness in middle 10, and salvation in last 10..

Edit: there is no du'a for salvation from hell fire mentioned in OP for last 10 days. One masnoon du'a is Allahumma ajirnaa min an-Naar (O Allah save us from the Fire)

The last du'a is extremely famous, and should be read especially when seeking laylatul qadr in last ten nights.

to OP for the reminder.