State Focus Haryana Institution Polity & Governance

Chandigarh, capital of two States and part of neither, is the principal seat of the Punjab and Haryana High Court

The page of the e-Committee of the Supreme Court of India on the Punjab and Haryana High Court records that it is the capital of two States of the Indian Union, namely, the Punjab and Haryana, and that although it is the capital of two states the city belongs to none of them and is a Union Territory. The page places Chandigarh 365 meters above the sea-level on the foot-hills of the Shivalik range.
The court descends from the High Court of judicature at Lahore. After Partition the East Punjab High Court of judicature was established at Shimla on August 15, 1947, by an order of the Governor General issued under Section 9 of the Indian Independence Act, 1947.
Shimla's winter was inconvenient for litigants, so the seat of the High Court was shifted to Chandigarh. The Court started functioning at Chandigarh from its present building with effect from January 17, 1955, and was formally declared open on March 19, 1955.
The building was planned by the French Architect Le Corbusier, who had earlier been chosen to execute the new capital project on a 114.59 sq.km. tract at the foot of the Shivalik Hills.
On the reorganisation that brought Haryana and the Union Territory of Chandigarh into existence, the High Court of Punjab was renamed as the High Court of Punjab and Haryana, and the principal seat of the High Court remained at Chandigarh.
The same page records that the sanctioned strength of the High Court is 38 permanent and 30 additional Judges, and notes the Open Hand, the official emblem of Chandigarh, standing in metal beside the High Court.

Principal seat: Chandigarh Earlier seat: Shimla Began sitting in the present building: January 17, 1955 Sanctioned strength recorded: 38 permanent and 30 additional Judges Architect of the building: Le Corbusier
Why it matters for exams: One High Court serving two States and a Union Territory, where it sits, and the fact that Chandigarh belongs to neither State are repeatedly asked in both Kerala PSC and UPSC prelims.
Kerala PSCUPSCSSC

In plain words

Union Territory Union Territory — A territory administered by the Union Government rather than by a State government of its own.

Principal seat Principal seat of a High Court — The main place where a High Court sits, as distinct from any bench set up elsewhere.