This is the 10463rd most frequent Russian word.
веткой
"Веткой" translates to "branch" (in the instrumental case) in English.
Here, 'веткой' refers to a physical object from a tree.
Он держал в руках старую ветку.
He held an old branch in his hands.
In this sentence, 'веткой' describes the habitat or location of the birds.
Птицы сидели на ветке у окна.
Birds were sitting on a branch near the window.
The word 'ветку' here is used in an artistic context, depicting a visual representation of the object.