Are there any specific duties that a Chief Justice or Judge of the Supreme Court of India must perform, according to their oath?
According to their oath, a Chief Justice or Judge of the Supreme Court of India must:

1. Bear true faith and allegiance to the Constitution of India as by law established.
2. Uphold the sovereignty and integrity of India.
3. Duly and faithfully perform the duties of their office without fear or favor, affection or ill-will.
4. Uphold the Constitution and the laws.