This is Annapurna, literally one who is full of food to give to her devotees. Normally she is shown with two hands, holding in one hand a jeweled vessel containing food and in the other a spoon to distribute the food.  In this case she has four hands, the rear hands hold Pasha (noose) and Ankusha (elephant goad). A rarer version.

Annapurna is associated with Siva and, in Nepal, she is sometimes represented as one of the consorts of Shiva. (T. E. Donaldson, Siva Parvati and Allied Images Vol I, Page 122). This example with Annapurna holding Pasha and Ankusha, two of Shiva’s attributes, corroborates that association.

The most famous temple for Annapurna is in Varanasi (Benares) and the temple dates back to the 18th century. Considering that Annapurna is associated with one of the basic needs, it is surprising that there are not many more temples dedicated to Annapurna.  

The idol is 6.5 cm in height and has worship related wear. This Vigraha maybe from Telugu speaking areas. This maybe dated to the eighteenth century.