Praise be to Allah.
The Prophet SAWS (peace and blessings of Allaah be upon him) used to sleep on his right side, putting his right hand on his right cheek, and this is what the Prophet SAWS (peace and blessings of Allaah be upon him) recommended others to do. According to a saheeh hadeeth narrated from al-Baraa’ ibn ‘Aazib, the Prophet SAWS (peace and blessings of Allaah be upon him) said: “When you go to bed, do wudoo’ as if for prayer, then lie down on your right side…” (Narrated by al-Bukhaari, al-Wudoo’, 239). The Sunnah is to put one’s right hand under one’s cheek. It was narrated that Hudhayfah (may Allaah be pleased with him) said, “When the Prophet SAWS (peace and blessings of Allaah be upon him) went to bed at night, he would put his hand under his cheek, then say, ‘Allaahumma bismika amootu wa ahyaa (O Allaah, in Your name I die and I live).’ Then when he woke up he would say, ‘Al-hamdu Lillaah alladhi ahyaanaa ba’da ma amaatanaa wa ilayhi al-nushoor (Praise be to Allaah who has brought us back to life after causing us to die, and to Him is the resurrection).’” (Narrated by al-Bukhaari, 6314).
Ibn Hajar said: The right side is singled out for a number of reasons, such as: this lets a person wake up more quickly; it also allows the heart to lean towards the right hand side. Ibn al-Jawzi said: the doctors have stated that this position is more beneficial to the body. They said to start by lying on the right for a while, then turn over to the left, because the former aids peristalsis and sleeping on one’s left side facilitates digestion.
Al-Nawawi said: this hadeeth mentions three acts that are Sunnah, the first of which is doing wudoo’ before going to sleep. If one already has wudoo’, there is no need to repeat it, because the aim is to go to sleep in a state of tahaarah (purity). The second is to sleep on one’s right side…
This indicates that sleeping on one’s right side is Sunnah, and if a person does that to follow the example of the Prophet SAWS (peace and blessings of Allaah be upon him), he will be rewarded for that. Sleeping on one’s left side is permitted, but one misses out on the reward for following the Sunnah. And Allaah knows best.