This is the 16743rd most frequent Turkish word.
yüzündeki
"On your face" or "on his/her/its face" (depending on context).
Here, 'yüzündeki' implies 'on your face,' qualifying the location of the 'yara' (wound).
Yüzündeki yara dikkatimi çekti.
The wound on your face caught my attention.
The word 'yüzündeki' here refers to 'on your face,' specifically describing the location of 'gülümseme' (smile), using Turkish possessive and locative suffixes.
Yüzündeki gülümseme onu çok güzel gösteriyordu.
The smile on your face made you look very beautiful.
In this sentence, 'yüzündeki' means 'on their face,' describing where the 'ifade' (expression) is located.