Officials said about 30 per cent voting was reported from Chikkodi-Sadalga and Shikaripura and 38 per cent in Bellary Rural, with the polling process being peaceful.
The three constituencies have a total electorate of over 5.57 lakh.
Today's elections are a litmus test for Chief Minister Siddaramaiah and BJP national Vice-President and former Chief Minister B S Yeddyurappa as this is the first electoral showdown after the recent Lok Sabha polls.
The Congress has gone all out not only to retain Chikkodi-Sadalga but also wrest from the BJP Bellary Rural and Shikaripura seat, where Yeddyurappa's son B Y Raghavendra is a candidate.
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Yeddyurappa had vacated the Shikaripura seat after his election to the Lok Sabha from Shimoga, which Raghavendra had earlier represented.
JDS, dogged by rumblings of discontent within over the leadership of its supremo Gowda and his son and former Chief Minster H D Kumaraswamy, has not fielded any candidates.