Hello,
When snapping a vertex, it snaps to vertices of the same object and the problem is, it also snapping to the vertices of the objects(shown in red arrow) which located behind the active object. How can I disable that. Any help would be greatly appreciated. Thank you.
You can turn off snapping to itself, but not snapping to other objects. If you only want to snap to the active object, I would recommend working on your mesh in local/isolation view (numpad /) or hide unselected objects (Shift H, in object mode).
Thank you.