This is the 10715th most frequent Turkish word.
damında
"On the roof of."
In this sentence, 'damında' means 'on the roof of' emphasizing a spatial relationship between the house ('ev') and its rooftop.
Kediler evin damında oynuyor.
The cats are playing on the roof of the house.
'Damında' here metaphorically refers to the 'top' or 'peak' part of something, in this case, the storybook.
Çocuklar masal kitabının damında yazılanları merak ediyor.
The children are curious about what is written at the top of the storybook.
This usage of 'damında' denotes presence and location, linking the shepherd's house to its roof area.