The identification as Venugopala (Krishna playing the flute) is based on his playing the flute. Venugopala is probably the only Hindu deity portrayed playing the flute.
Venugopala is seated on a two-level lotus Padmasana. This is adult Krishna and is fully clothed. Note the side tassels, central fold and shoulder cloth. The ornamentation is complete and the earrings merit attention.
An unusual aspect of this Vigraha is the inverted lotus above his head, protecting him like an umbrella would. On the lotus above his head, two levels of petals are chased. It is the care for details and good craftsmanship that got my attention.
It is unusual for the flute to be present. In this case, it is for sure the original one.
The Vigraha is about 10.5 cm in height. It is, most likely, from the Mysore region of Karnataka. Though the bottom is worn, there is only light wear on his face. It may be dated to the nineteenth century.
Added to the collection for the craftmanship, the flute, the lotus ‘umbrella’ and the unusual iconography (seated Venugopala).
This blog site has one more seated Venugopala without the flute.