Short answer
No. If you make a mistake while following the imam, such as forgetting a tasbih or a wajib, you do not do sajdah sahw; the imam carries it. But if the imam does sajdah sahw, you must do it with him, even if you did not notice his mistake or joined after it. A latecomer does his own sahw only for mistakes in the part he completes alone.
The follower has no sajdah sahw for his own forgetfulness behind the imam. When the imam makes sahw, following him in it is wajib on all followers, including the latecomer (masbuq), who joins the imam in the sahw and then stands to complete his prayer.
The four schools agree on this.
Explanation
The Prophet ﷺ said the imam is a guarantor, and that the imam is appointed to be followed, so do not differ from him. On this basis the four schools agree that the imam carries the follower's minor slips, and that the follower must follow the imam in his sajdah sahw.
- Your own mistake behind the imam: for example you forgot to recite the tashahhud fully, or you said a tasbih in the wrong place. No sahw. If you missed a fard act yourself, such as a sajdah, make it up straight away and catch up with the imam.
- The imam's mistake: when he does sahw, do it with him. Do not do it if he does not.
- You think the imam forgot something: prompt him with "SubhanAllah"; see how to correct the imam. If he carries on, follow him.
If you joined late (masbuq):
- When the imam gives the first salam for sahw, do not give salam with him. Make the two sajdahs of sahw with him, sit, and then when he gives the final salams, stand to complete your missed rakats.
- If you mistakenly gave salam with the imam's sahw salam, you have not left the prayer; stand and complete.
- If you make a mistake in the rakats you complete alone after the imam has finished, you are now praying alone, so do your own sahw at the end.
See joining the prayer late, forgetting sajdah sahw and the full method in sajdah sahw.
The evidence
Sunan Abi Dawud 517
Grading to be checked... الإمام ضامن والمؤذن مؤتمن ...
"The imam is a guarantor and the mu'adhdhin is entrusted."
The imam carries responsibility for the followers' prayer.
Sahih al-Bukhari 722
Sahih... إنما جعل الإمام ليؤتم به فلا تختلفوا عليه ...
"The imam is appointed to be followed, so do not differ from him."
The follower follows the imam in sahw and does not add his own.
Where the ruling is recorded
- al-Hidaya, Kitab al-Salah, chapter on sajdah sahw. If the follower forgets, there is no sahw on him or the imam; if the imam does sahw, the follower must do it with him.
- Radd al-Muhtar (Ibn Abidin), Kitab al-Salah, chapter on sajdah sahw. The masbuq follows the imam in sahw and does his own for mistakes while completing.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.