How to implement this blur effect do not use drop shadow in photoshop?

A lot of the time it works out better to make your shadows manually.

Make a new layer beneath the object layer.

Control click the object layer's thumbnail to load it as a selection, and fill the selection with black in the new layer you just made.

This has several advantages over a layer style drop shadow.  It's still nondestructive, and you can move it, apply blur.  The biggest advantage is that you can mask part of your shadow layer.  I use the Smudge tool a lot to fine tune shading layers — you can't do that with a layer style.

You can use cool  effects like Path Blur on your shadow

You can make your shadows something other than boring black, use other filter effects (in case your shadow exists in a whole other universe).