Salamu alaykum Please, what is the legal opinion on someone praying nawafil while also praying Qasri and he is on a journey. Please, I need evidence from qur`an, sunnah and it should quoted.

Wa alaykom assalam

The desirability of performing optional prayers while traveling is a debatable issue between the different juristic schools.  No indication in the Quran regarding this point.  In the Sunnah, it is narrated that the prophet (PBUH) did not quit praying -even while traveling-; Sunnat Al-Fajr and Salatu Al-Witr.  As of the rest of them, no direct and clear evidence to the best of my knowledge.  Most likely, they are waived.