This is the 13509th most frequent Polish word.
pewnemu
"Certainly" or "to a certain" (depending on context).
The word 'pewnemu' in this context is a dative case of 'pewien' which means 'a certain'. It modifies 'psu' (dog) to indicate a specific, though unidentified, entity.
Pewnemu psu udało się uciec z podwórka.
A certain dog managed to escape from the yard.
Here, 'pewnemu' is again functioning as a dative case modifier for the noun 'człowiekowi' (man), indicating an unspecified individual referred to contextually.
Pewnemu człowiekowi podano kawę.
A certain man was served coffee.
In this sentence, 'pewnemu' modifies 'znajomemu' (acquaintance) in the dative case, specifying an acquaintance without detailing exactly who they are.