He fished a bit of paper from his pocket and studied it.

[Jardino]

Topic
He fished a bit of paper from his pocket and studied it.
Matilda by Roald Dahl

Does that fish means "search" right? -
[ I usually + adv/prep ] to try to find something, using your fingers to look for it: ex)The director was fishing for information about our strategy. from cambridge dictionary
But, there's a object... a bit of paper... what is that?

 

[entangledbank]

When there's a direction like 'fished out' or 'fished from his pocket', it means he found it and took it out. So it has an object. If he is only searching, he is fishing around, or fishing in his pocket. (He doesn't take something out/from somewhere.)

 

[Myridon]

Words are often used in more than one way.
fish - WordReference.com Dictionary of English

3 to draw or pull out as if fishing:[~ + object (+ out of + object)]He fished a coin out of his pocket.
4 to seek to obtain something indirectly:[~ + for + object]fishing for a compliment.

The first sentence is an example of definition 3.
The second sentence is an example of definition 4.

 

[Jardino]

When there's a direction like 'fished out' or 'fished from his pocket', it means he found it and took it out. So it has an object. If he is only searching, he is fishing around, or fishing in his pocket. (He doesn't take something out/from somewhere.)

[ I or T ] to catch fish from a river, sea, lake, etc., or to try to do this: from cambridge
This is very usual meaning about fish verb. According your explaining , the meaning fish about my sentence is developed by this.

 

[Myridon]

[ I or T ] to catch fish from a river, sea, lake, etc., or to try to do this: from cambridge

The Cambridge Advanced Learner's Dictionary has other definitions of "fish."
FISH | meaning in the Cambridge English Dictionary