Can You Offer Sujud As-Sahw in Sunnah Prayer?
Question

Is it correct to do Sujud As-Sahw (prostration of forgetfulness) in a Mustahabb prayer such as a Nafl prayer?
Praise be to Allah.It is prescribed to do Sujud As-Sahw in Nafl (supererogatory) prayers just as it is prescribed to do it in the obligatory prayers when there is a reason for doing it. 
This is the view of the majority of scholars ancient and modern, because of the general meaning of the words of the Prophet (peace and blessings of Allah be upon him): “If any one of you forgets [something in the prayer], let him do two prostrations.” (Narrated by Muslim, 402)
Also, correcting the prayer and annoying the devil are things which may be needed in the Nafl prayers just as in the obligatory prayers. 
Some scholars – including Ibn Sirin, Qutadah, ‘Ata’ and a number of the companions of Ash-Shafi’i scholars (may Allah have mercy on them) were of the view that there is no Sujud As-Sahw in voluntary (Nafl) prayers. But the correct view is that of the majority. 
Al-Bukhari (may Allah have mercy on him) said in his book: “Bab As-Sahw fi’l-fard wa’l-tatawwu’ (Chapter on forgetfulness in obligatory and voluntary (prayers)). Ibn ‘Abbas (may Allah be pleased with him) did two prostrations after Witr, and Ibn Hajar (may Allah have mercy on him) said in Al-Fath, commenting on the report of Ibn ‘Abbas: this was narrated by Ibn Abu Shaybah with an authentic Isnad (chain of narration). 
The point of quoting what Ibn ‘Abbas (may Allah be pleased with him) did, is that Witr is not obligatory, but Ibn ‘Abbas did Sujud As-Sahw in it, which indicates that Sujud As-Sahw should be done in both obligatory and Nafl prayers. 
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said: “Sujud As-Sahw is two Sajdahs (prostrations), and should be done in both obligatory and Nafl (supererogatory) prayers if there is a reason for doing it.” (Majmu` Fatawa Ibn ‘Uthaymin, 14/68) (See Kitab Sujud As-Sahw fi Daw’ Al-Kitab wa’s-Sunnah Al-Muttaharah by Shaykh ‘Abdullah At-Tayyar)
And Allah knows best.