Answered by Mufti Mohammed Tosir Miah
Question:
Duas in Sajdah
Answer:
The Sajdah is one of the compulsory acts of salah without which a person’s salah will be deemed invalid. The sajdah also is one of the most submissive positions. It is the best occasion to ask Allah 
for something and seek tawbah and istighfar and refuge from the Fire of Hell. It is because of this reason there are many narrations regarding the various duas and supplications one can make in this state. The Prophet of Allah 
use to make dua and cry in Sajdah.
Saaiduna Ibn Abbas 
reported that the Prophet of Allah said “… [While] prostrating yourselves be earnest in supplication, for it is fitting that your supplications should be answered.”
(Sahih Muslim)
Saaiduna Abu Hurairah reported that the Prophet of Allah said, “The servant is nearest to his Lord when he is prostrating to Him, so make supplication in this state.” (Sahih Muslim)
Only Allah Knows Best
Mohammed Tosir Miah
Darul Ifta Birmingham