This is Yoga Dakshinamurti, a form of Siva. The attribution to Siva is based on the battle axe and antelope in his rear right and left hands respectively. The Yogapatta running around him and the way he is sitting leads to the prefix, Yoga. The lower right hand in cin mudra (preaching or espousing) identifies him as Dakshinamurti.
Siva as a teacher of Yoga, music, dance, other arts and science is known by the name Dakshinamurti. One other account is Siva in this form, is normally found in the walls of the temple facing South. Dakshina means South.
There are four different forms of Dakshinamurti, Yoga, Vina, Janana and Vyakhyanamurti (Expounder of Vedas).
The Yoga position, in turn, has three forms with legs crossed (as in the image above), with right leg pendant and the left leg placed over the right and the third with both the legs raised and held in place by Yogapatta (Utkutikasana). A Narasimha in the third form is on this blog site. See Yoga Narasimha.
Examples of this form of Yoga Dakshinamurti are given in Elements of Hindu Iconography by T A G Rao (Vol Two, Part 1, Page 286) and Siva Parvati and Allied Images by T E Donaldson has two related examples (Volume 2 C1-page 1 and Fig 1 Page 122).
One interesting aspect of this bronze is Siva’s hair arrangement. It seems to suggest this bronze is from Kannada speaking region. I have come across few Ved Vyasa bronzes with similar hair arrangement.
The bronze is about 5.5 cm in height and may date to the 19th century or earlier.
This is one of the rare bronzes in my collection. So far I have not come across another bronze of this iconography.
10 Mar 2017: One of the senior collectors, HJH, pointed out this Yoga Dakshinamurti does not have any of the typical attributes Kamandala, Akshamala, fire and snake. But instead carries the attributes of Chandrasekhara, another form of Siva, namely battle axe and antelope. Despite the identification in the references quoted, this may be a different form of Siva. HJH’s view is the reason behind the tentativeness in the title of this blog. All comments are welcome.