First, second and third 10 days of Ramdhan

First ten days (1-10) of the Blessed Month of Ramdhan are the days of Mercy. So we should seek Allah's Mercy in these days.
Rab-bigh-fir war-ham wa Anta Khair-ur-Raahimeen. (Surah Al Muminun:118) Meaning: My Lord! Forgive and have mercy, for You are the Best of those who show mercy! Ya Rabb, Allahumma arhamni Ya Arham-mar-Rahimeen.
Ya
Hayyu Ya Qayyumu Birahmatika astaghees.

The second ten days (11-20) of Ramdhan are the days of Forgiveness.So we should seek Allah's forgiveness and repent for sins in those days.
Allahum-magh-fir-li dhunoobi Ya Rabbal Alameen
Rabbana Fagh-fir-lana dhunoobana wa kaf-fir-'anna sayyi-aatina wa ta-waf-fana ma-'al abraar. (Surah Al-Imran:193)
Meaning: Our Lord! Forgive us our sins and remit from us our evil deeds, and make us die in the state of righteousness along with Al-Abrâr (those who are obedient to Allâh and follow strictly His Orders).

The last ten days (21-30) of Ramdhan are to seek Refuge in Allah from the Hellfire.
Allahumma Ajirna min-an-naar.
Meaning: O Allah, protect us from the fire.