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A perfectly diamagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field $$\vec{B}$$. Then the field inside the paramagnetic substance is:
Magnetic permeability of a perfect diamagnet: $$\mu_r = 0$$
Magnetic field inside the bulk diamagnetic material: $$B_{\text{inside}} = \mu_r B = 0$$
Since the external magnetic field lines cannot penetrate the perfectly diamagnetic outer sphere, no magnetic flux reaches the inner cavity.
$$\text{Field inside the central cavity} = 0$$
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