Once I add a bezier circle, there is no option to change the number of vertices anywhere. As you can see, the box at the bottom has no option to add vertices. If I click edit mode, the bottom box also disappears. I am a beginner in blender so a detailed reply will be helpful. Also, once the circle is added, I have pressed F6 (as suggested in other answers) but nothing happened.
You have added a curve circle, instead of a mesh circle. A curve circle does not have vertices, it has control points, but these cannot be adjusted when adding the object. A mesh circle will have the option to adjust the number of vertices.
Press Shift+A> Mesh> Circle to add a mesh circle. Then the Adjust Last Operation panel (the panel in the bottom left) will show the option to adjust the vertices.