Story of origin of Veni River is associated with a curse by Goddess Saraswati. Legend has it that Brahma was ready to perform a yajna. Vishnu and Shiva arrived to witness the yajna. But Brahma could not start the yajna as his wife Saraswati did not turn up.
As the auspicious time was passing over, at the instance of Shiva, Brahma started the yajna with his second wife Gayatri.
But soon Goddess Saraswati arrived at the yajna and got angry for not waiting for her.
She cursed the gods present there to take the form of rivers.
Thus Shiva was cursed by Goddess Saraswati to take the form of Veni River.