The Holy Prophet (peace be upon him and his progeny) has said:
It (Ramadan) is the month, whose beginning is mercy, its middle, forgiveness and its end, emancipation from the fire (of hell)
I found some sites that had the duas that are recommended to say during each third (ten days) of the month of Ramadan. I will post them below Insha Allah.
1st -10 days of Ramadhan recite dua above for mercy
11th -20th days of Ramadhan recite dua above for remission for Sins (forgiveness)
21st to last ten days of Ramadhan recite dua above for free from Hell recite this dua in plenty for safety from hell