Step 1: Constitutional Basis.
Article 215 grants High Courts the status of a Court of Record and the power to punish for contempt of itself and of subordinate courts. Similarly, Article 129 grants the same power to the Supreme Court.
Step 2: Why subordinate courts cannot punish contempt.
Subordinate courts are not Courts of Record and therefore cannot exercise contempt jurisdiction independently. A judicial officer cannot punish contempt of his own court except where statutes expressly provide minor powers.
Step 3: Role of High Court.
When contempt occurs against a subordinate court (e.g., insulting a magistrate or obstructing a trial), the High Court exercises jurisdiction to punish the contemnor.
Conclusion:
Hence the correct position is that the respective High Court handles contempt proceedings for subordinate courts.