Praise be to Allah.
Sunnah way of sleeping
The Prophet (peace and blessings of Allah be upon him) used to sleep on his right side, putting his right hand on his right cheek, and this is what the Prophet (peace and blessings of Allah be upon him) recommended others to do.
According to an authentic hadith narrated from al-Bara ibn ‘Azib, the Prophet (peace and blessings of Allah be upon him) said: “When you go to bed, do wudu as if for prayer, then lie down on your right side…” (Narrated by al-Bukhari, al-Wudu, 239)
The Sunnah is to put one’s right hand under one’s cheek. Hudhayfah (may Allah be pleased with him) said, “When the Prophet (peace and blessings of Allah be upon him) went to bed at night, he would put his hand under his cheek, then say, ‘Allahumma bismika amutu wa ahya (O Allah, in Your name I die and I live).’ Then when he woke up he would say, ‘Al-hamdu Lillah alladhi ahyana ba’da ma amatana wa ilayhi al-nushur (Praise be to Allah who has brought us back to life after causing us to die, and to Him is the resurrection).’” (Narrated by al-Bukhari, 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 hadith mentions three acts that are Sunnah, the first of which is doing wudu before going to sleep. If one already has wudu, there is no need to repeat it , because the aim is to go to sleep in a state of purity. The second is to sleep on one’s right side…”
Is it permissible to sleep on your left 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 (peace and blessings of Allah 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 Allah knows best.