I saw the Messenger of Allah ﷺ supplicating like this, with the inside of his palms and their outside.
حدثنا عقبة بن مكرم حدثنا سلم بن قتيبة عن عمر بن نبهان عن قتادة
رأيت رسول الله ﷺ يدعو هكذا بباطن كفيه وظاهرهما
No references are available.
Graded, its chain is daif. Umar bin Nabhan is daif, and Ibn Main, Abu Hatim, and others declared him daif.