How to select some specific1 anchor points of many polygons?

Dincer, if all you really want is a spiral, I would use the Spiral Tool as Jacob suggested.

I was able to recreate your spiral by using these settings.

K

Dinçer,

I wonder whether the most straightforward way could be to simply use the Spiral Tool with the right settings which depend on the exact kind of spiral, see Draw Spiral here,

https://helpx.adobe.com/illustrator/using/drawing-simple-lines-shapes.html

Dinçer,

as far as I can see, based on the example you provided, currently there are no automated ways to do the desired selections in one shot.

But: There may be some other routes to do what you want without having to click with the Pen tool thousands of times.

To check that, can you please share a sample Illustrator file with some instructions that explain your final goal?

Dinçer Dinç,

How about the Lasso Tool (after locking any objects with Anchor Points that may get in the way, such as maybe (the top Anchor Point of) the circle in the centre)?

https://helpx.adobe.com/illustrator/using/selecting-objects.html