This is Yoga Dakshninamurti. There are fewer doubts about attributing that name to this form of Shiva. Holding battle axe in his upper right hand, with his right leg hanging down and resting on Apasmara, his left leg resting on his right thigh, lower left hand in Cin mudra or Updesha (preaching) pose, his hair spread out like a flame(Jatta mandala), it is Shiva as Dakhinamurti. Here he is seated on a Padmapeetha rather than on a rock or hill.
Now to the Yoga part of his name. The band running around him resembles Yogapatta and hence the Yoga in his name. The band is actually a snake, see the hood rising between his left feet and left knee. The frontal image shows the snake’s tail going over its body. This Naga-pata makes this Yoga Dakshinamurti a very rare icon.
H K Sastri’s book on South Indian Images of Gods and Goddesses has two examples of Yoga Dakshinamurti (Figures 56 and 57). The attributes differ.
This bronze is only about 5.5 cm in height and shows significant ritual wear and bronze loss.
This is from Tamil speaking part of South India and may date to the sixteenth century. A delightful piece and it was an instant purchase.