"Whoever says 'Bismillah' 21 times before falling asleep, Allah tells the angels to write down a good deed for every breath he takes." Is this authentic? Is there Hadith or Quran about this?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

In the reliable Sunnah literature that we have at hand, we have not come across any Saheeh (sound), or a Dha’eef (weak) or Mawdhoo' (fabricated) Hadeeth in relation to what you mentioned.

Also, there is nothing in the Quran with this meaning.

Allaah Knows best.