What is the basis for the sunnah prayers performed together with the obligatory prayers?

The Prophet Muhammad (peace be upon him) performed sunnah prayers before and after the obligatory prayers and also recommended them to his community. For this reason, it is encouraged to perform the regular (rawatib) sunnah prayers together with the obligatory prayers as much as possible. In one of his hadiths, the Prophet (peace be upon him) said, “Whoever consistently performs twelve units of sunnah/voluntary prayers—four before Dhuhr, two after Dhuhr, two after Maghrib, two after ‘Isha, and two before Fajr—Allah will build a house for him in Paradise.” (Tirmidhi, Salat, 306 [414]; see also Muslim, Salatu’l-Musafirin, 101 [728]). Regarding the Asr prayer, he said, “May Allah have mercy on the one who performs four units of prayer before Asr.” (Abu Dawud, Tatawwu‘, 296 [1271]; Tirmidhi, Salat, 318 [430]).

In another hadith, he said: “On the Day of Judgment, the first thing a Muslim servant will be called to account for is the obligatory prayer. If he has performed them completely, that is excellent. If not, it will be said: ‘See if My servant has any voluntary prayers.’ If he has voluntary prayers, the deficiencies in the obligatory prayers will be completed with them. The same will be done for the other obligatory acts.” (Ibn Majah, Iqamatu’s-Salawat, 202 [1425]; see also Abu Dawud, Salat, 148 [864]).

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu