of asking for forgiveness?
Allah SWT has preserved many prayers in Quran for the benefit of people to come. These are prayers of prophets who were near & dear to God. Best is to learn these prayers (Arabic & their meaning) and recite 'em whenever you have time to yourself & in regular namaz as well.
But they who repent and amend and openly declare the truth, it is these to whom I turn with forgiveness, and I am Oft-Returning with compassion and Merciful. (Al Baqarah - Verse 160/161)
And those who, when they commit a foul deed or wrong themselves, remember Allah and implore forgiveness for their sins and who can forgive sins except Allah? and do not persist knowingly in what they have done. (Al-'Imran, Verse 135/136)
Use any Quran search engine online and search for words forgiveness or forgive, & you will have many prayers. Here is one of my favorite prayers;
*Allah burdens not any soul beyond its capacity. It shall have the reward it earns, and it shall get the punishment it incurs. Our Lord, do not punish us, if we forget or fall into error; and our Lord, lay not on us a responsibility as Thou didst lay upon those before us. Our Lord, burden us not with what we have not the strength to bear; and eface our sins, and grant us forgiveness and have mercy on us; Thou art our Master; so help us Thou against the disbelieving people. *(Al-Baqarah, Verse : 286/287)