1. Interpret the setup

   • The outer sphere is perfectly diamagnetic.
   • A perfectly diamagnetic material behaves like an ideal diamagnet (similar to a superconductor for magnetic response), so the magnetic field inside it is $\vec B = 0.$
   • There is a small spherical cavity at the centre, and that cavity is filled with a paramagnetic substance.
   • The whole system is placed in an external uniform field $\vec B$.

2. Key idea: shielding by a perfect diamagnet

   A perfect diamagnet expels magnetic field from its interior. Therefore, inside the body of the diamagnetic sphere, $\vec B = 0.$

   Since the cavity is completely enclosed by the perfectly diamagnetic material, the external magnetic field cannot penetrate through the surrounding perfect diamagnet to reach the cavity.

3. What happens inside the cavity?

   The cavity is at the centre and is surrounded on all sides by the perfectly diamagnetic material. Because the magnetic field in the surrounding medium is zero, the cavity is effectively magnetically shielded.

   Hence the magnetic field inside the cavity is also $\vec B = 0.$

4. Role of the paramagnetic substance

   A paramagnetic substance gets magnetized only when subjected to a magnetic field. But here the applied field does not reach the cavity, so there is no magnetic field available inside to magnetize it.

   Therefore, the field inside the paramagnetic substance remains $\boxed{0}.$

5. Check options

   • A: $\vec B$ — incorrect
   • B: zero — correct
   • C: much larger than $|\vec B|$ and parallel — incorrect
   • D: much larger than $|\vec B|$ but opposite — incorrect

Therefore, the correct option is $\boxed{\text{B}}.$