If I joined Jamaat prayer (say Asar) when the imam is at his third Rakah, do I read a Sura after al-Fatiha or not because the imam would have already done the first Attahiyyat?

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

The Prophet said: “When you hear the Iqaamah, proceed to the prayer with calm and dignity and do not rush. Pray what you can (in congregation) and complete what you have missed.” [Al-Bukhari and Muslim]

The person who joins the congregational Prayer after the Imam has prayed a Rak’ah or more should first say the opening Takbeer (Takbeeratul Ihraam) while standing and then should move directly to perform the act that the Imam is performing, and when the Imam finishes the Prayer, he (the person who joined the Prayer late) should complete what he has missed. The words of the above Hadeeth prove that the portion of the Prayer this person has performed with the Imam is the first part of his Prayer and what he performs after the Imam has finished is the remaining part of his Prayer. For instance, if one catches up with the Imam after the latter has performed two Rak’ahs, then the former has to perform yet another two Rak’ahs, when the Imam finishes his Prayer. In these two Rak’ahs he has to recite Soorah al-Faatihah only. If one catches up with the Imam only one Rak’ah from the Prayer of Thuhr, ‘Asr or ‘Isha, he has to perform three more Rak’ahs right after the Imam finishes the congregational Prayer. In the first Rak’ah, he should recite Soorah al-Faatihah and another Soorah and should sit for Tashahhud. In the second and third Rak’ahs, he has to recite Soorah al-Faatihah only and should not sit for Tashahhud between these last two Rak’ahs. There are many other opinions concerning this issue but what we mentioned here is the preponderant one.

For more benefit on joining the prayer late, please refer to Fataawa 181353, 88883, 352786, 5502, 6182 and 68550.

Allah knows best.