In the name of Allah, the most Beneficent, the most Merciful.
It has been narrated that the Propeht of Allah Sallalhu Alayhi Wasallam used to eat with his thumb, index finger and middle finger and he licked his middle finger first, then index and finally his thumb. (Tabraani)
If there is food stuck on the other fingers like little finger or the ring finger, then one should start licking it from there.
Only Allah Knows Best
Mohammed Tosir Miah