I want to know that how to get coordinates of edge centers(like bottomCenter, topcenter etc) in godot.
It's hard to answer the question without more detail.
In the case that you literally just want the positions of the edge, you can add half the width. to the position. If you provide code, you'll get a more useful answer.
right_center = sprite.global_position + new Vector2(sprite.sprite.texture.get_width(), 0)
top_center = sprite.global_position + new Vector2(0, sprite.sprite.texture.get_height())
This is not exactly what you asked, but you could also consider modifying the Offset Property of Sprite. This changes the draw position of that sprite.
Similarly, you can check centered to false, which behave similarly.
For example, I'm assuming you have a node representing a tree stump, and when you add a sprite at that stump's position, it puts the center of the sprite at the location of the tree stump node, possibly clipping through the ground. (note: screenshots Godot 4, but the docs I linked above are Godot 3.5)
You can add an offset to the stump, it can still be positioned along the floor, but be drawn above it.