Days 1 to 10 · First ashra
Popularly called the ten days of mercy (rahmah). The popular dua for it, Rabbighfir warham wa anta khayrur-rahimin, is from the Quran, but no hadith ties it to these days.
وَقُل رَّبِّ ٱغْفِرْ وَٱرْحَمْ وَأَنتَ خَيْرُ ٱلرَّٰحِمِينَ
Wa qur Rabbigh fir warham wa Anta khairur raahimeen
"And, [O Muhammad], say, "My Lord, forgive and have mercy, and You are the best of the merciful.""
Quran 23:118, translation by Sahih International.