Are Andaman and Nicobar islands in Indian ocean a continuation of Alpide-Himalayan orogeny or are they volcanic in origin?
The Andaman and Nicobar Islands are neither orogenic or volcanic in origin. They are in fact an accretionary wedge, i.e. an accretion of sediments and oceanic crust "scraped" from the subducting Indian plate. See for instance the description in the first chapter of the aptly titled The Andaman–Nicobar Accretionary Ridge:
The islands are an exposed segment of the accretionary wedge (outer arc) of the Sunda subduction system, where the Indian Plate subducts beneath the Sunda Plate. Ongoing uplift of the sediment-dominated accretionary wedge has exposed, over a relatively small area, a diverse range of rock types associated with the subduction complex (dismembered ophiolites, volcanic-arc rocks, trench-slope deposits, submarine fan turbidites, pelagic sediments and the sediments of shelf and reef environments), making it an ideal area for investigating subduction processes.
(Unfortunately, other chapters with more detailed descriptions are not open access.)
Note that if some of the sediments are indeed volcanic in origin, it does not mean that volcanism is responsible for building the archipelago, like it was for the Chagos-Laccadives ridge for instance, to stay around India. It is the accretion of sediments in the subduction trench, and their subsequent uplift above the sea, that created the islands.
The Andaman and Nicobar Islands are partly volcanic in origin. This volcanism is caused by the subduction of the Indo-Australian Plate beneath the Burman Plate, which is an extension of the much larger Sunda plate to the east. This produces large scale volcanism throughout the Indonesian Archipelago as well as the Andamans, but is too far away from Borneo to induce volcanism there. The subduction also has a lifting and thickening effect on the margins of the upper plate, which assists in the process of raising islands and mountains. The most active volcano in the Andamans is Barren Island.