This is Durga, identified by her attributes and the vahana.
The four-armed goddess is sitting in Ardhapadmasana on a lotus base which in turn is supported by a rectangular base.
Her upper hands are holding Chakra (discuss) and Shankha (conch shell) and her lower hands are in Abhaya and Varada mudra (protection and boon bestowing).
Her vahana, a lion, is in the front of the pedestal. Goddess holding Shankha and Chakra could be Vaishnavi. But it is her vahana, lion, identifies her as Durga. Durga is framed by a very simple prabhavali (no Makara, no cobra and no Kiritimukha). Unusual.
There is a lot of age to this bronze. The lion’s feature is typical of Hoysala. Going by the design of the Shankha suspect this may pre-date Hoysala period. The patina, crustation and prabhavali design support that date.
This bronze is about 9 cm in height and it is from North Deccan. The main idol and the base appear to have been cast together.
Some features that may help in dating are the tiered crown, narrow waist, the necklace falling between her breasts, minimal working on the back and, of course, the features of the lion.
2 Feb 2021: Chinmaya, through Facebook, pointed out Sri Mookambika of Kollur has the same attributes and vahana. Possibly the local name for Durga with its own Sthalapurana.