بسم الله الرحمن الرحیم
The phrase Assalatu Khairum Minan Naum (Prayer is better than sleeping) was not part of the azan (calling for prayer) during the time of the Holy Prophet (PBUH) and it has been included in Azan later (1). Furthermore, Imam ash-Shafi‘i says in his Kitab al-Umm as such:
"أكره في الأذان الصلوة خير من النوم لأن أبا محذورة لم يذكره."
It is not pleasing for me to say "Assalatu Khairum Minan Naum" in the Azan of the prayer, because Aba Mahzureh has not brought this phrase in his hadith.(2)
In fact it was Umar Ibn Khattab who ordered to include the phrase, "prayer is better than sleep" (Assalatu Khairum Minan Naum) in the Azan at Fajr.(3)
There are other documents to prove the fact that "Assalatu Khairum Minan Naum" was later added to the Azan. I just mention two of them:
اِن المؤذن جاء الي عمربن الخطاب يؤذنه لصلاة الصبح فوجده نائماً فقال:
الصلاة خير من النوم فأمره أن يجعلها في نداء الصبح.
The azan reciter went to Umar Ibn Al-Khattab informing him the Fajr prayer time, He found Umar Ibn Al-Khattab asleep, so he shouted "Assalatu Khairum Minan Naum". Umar, ordered to include it in the azan.
الصلاة خير من النوم، ولا نقول بهذا ايضا لأنه لم يأت عن رسول اللّه -
صلي اللَّه عليه و سلّم .
We don't admit "Assalatu Khairum Minan Naum", and also we don't say
that because this is not from the Prophet (PBUH).
Finally, Assalatu Khairum Minan Naum is used only for the Fajr prayer because it was included by Umar Ibn Al-Khattab in the Azan at Fajr.
1- Kanz al-Ummal by Ali ibn Abd-al-Malik al-Hindi, “kitab as-salah,” vol. 4, p. 270.
2- Quoted from Dalilo-Sidgh by Mohammad Hassan Mozaffar, Vol. 3.
3- Al-Musnad of Ahmad Ibn Hanbal, Vol. III, p. 408; Sahih Muslim, Vol. III, p. 183; al-Halabi, Al-Sirah, Vol. II, p. 105; Ibn Kathir, Vol. III, p.23.