During Sunnah prayers do you have to recite a Surah after Surah al-Fatiha in the third and forth Rak'ah?

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

A person performing optional prayers should recite a Chapter after the Faatihah in each and every Rak’ah, whether he prays two Rak’ahs or 4 Rak’ahs.

However, the majority of the scholars are of the opinion that optional prayers should be performed in twos. 

The evidence about this is in the Hadeeth narrated by Al-Bukhari and Muslim, which reads: "The prayer of the night is in twos."; and also in the Hadeeth of Al-Sunan and Musnad which reads: "The prayer of the night and the day is in twos and twos….etc." [Al-Albaani said that this Hadeeth is Sound]

Another evidence could be found in the saying of 'Aa'ishah who said that the Prophet used to pray 11 Rak’ahs between Isha and Fajr and he used to say ‘Salaam’ after every two Rak’ahs, and then pray one Rak’ah for Witr." [Abu Daawood]

Ibn Hajar, said: "This Hadeeth fulfilled the conditions of the two Shaykhs (meaning Al-Bukhari and Muslim)".

The concordance between the previous Ahadeeth and what 'Aa'ishah   said is in the Hadeeth narrated by Al-Bukhari and Muslim: "He used to pray four, how good and long they were", meaning that he used to pray four, but says Salaam after every two Rak’ahs.

Therefore, the Prophet used to pray optional prayers in twos (2-2 Rak’ahs).

Hence, if the questioner meant to pray Witr in three Rak’ah, or 5 Rak’ah with only one ‘Salaam’, then it is permissible not say ‘Salaam’ after the second Rak’ah, because the Prophet used to do so, as in the Hadeeth by 'Aa'ishah that he used to pray Witr in 5 Rak’ahs and did not use to say Salaam except in the last Rak’ah. This Hadeeth was narrated by Ahmad and An-Nasaa’i, and Al-Arnaout and Al-Albaani said that 'it was authentic.'

Allaah Knows best.