Solution:

Pondichiri – Under Chennai High Court

Andaman & Nicobar Islands- Calcutta Highcourt

Chandigarh- Chandigarh(Common high court for Punjab, Hariyana and Chandigarh(UT))

Delhi, which is also known as the National Capital Territory of Delhi (or NCT) is the only Union Territory, which has its own high court.
As far as the other Union Territories are concerned, they share their jurisdiction with some other States.
Chandigarh, which is also an Union Territory, houses the Punjab and Harayana High Court. The said High Court has the jurisdiction over the Union Territory of Chandigarh, State of Punjab and State of Haryana.