Union Government
(1) Appointments of Supreme Court officers/staff are made by the Chief Justice of India (or a Judge/officer he directs), subject to a possible presidential rule requiring UPSC consultation for outside appointments. (2) Conditions of service for such staff are prescribed by rules made by the Chief Justice (or an authorised Judge/officer), with salary/allowance/leave/pension rules requiring presidential approval. (3) The Supreme Court's administrative expenses, including staff salaries and pensions, are charged on the Consolidated Fund of India, and any fees the Court collects form part of that Fund.
The Chief Justice of India, not the executive government, controls hiring and administration of the Supreme Court's own staff - reinforcing the Court's independence from the government even in its internal administration. The Court's running costs are guaranteed funding from the Consolidated Fund as "charged" expenditure, insulating it from budgetary pressure by the government of the day.
This is part of why the judiciary is considered institutionally independent from the executive - even the people who staff and administer the Supreme Court's own registry report to the Chief Justice, not to any government ministry.