The coastal State/Union Territory of Bay of Bengal is :

A State or Union Territory is said to lie on the Bay of Bengal when its physical boundary touches India's eastern seaboard; the western-seaboard States instead border the Arabian Sea, and some States/UTs are entirely landlocked with no coastline at all.

Odisha lies on India's eastern seaboard, between West Bengal and Andhra Pradesh, and its coastline runs along the Bay of Bengal.

• Karnataka lies on India's western seaboard, on the Karnataka (Kanara) coast, bordering the Arabian Sea.

• Kerala lies on India's south-western Malabar coast, also bordering the Arabian Sea.

• Telangana, formed in 2014 by the bifurcation of Andhra Pradesh, is entirely landlocked with no coastline.

Among these four States, Odisha's coastline is the one that lies on the Bay of Bengal, matching the criterion asked for in the question.