Iam attempting to extrude in Z Axis iam pressing E+G+Z but I can't extrude the plane.
I am following this tutorial: https://youtu.be/OHg-CHcflPM?t=1299.
The E shortcut is for the "Extrude Region and Move".
The move (or grab) command you are trying to recall with G is alredy active. So by pressing G, you are activating the Vertex Slide option of the grab command.
Just press E and then Z to restrict the movement because you are already grabbing the object around.
Or yuo can press E and then Esc to Extrude the region only. After that you can activate the grabbing with G and restrict the movement with Z.