Vinayaki the female version of Vinayaka( Shri Ganesha).This Devi is worshiped in Hinduisms, Jainism and Buddhism in different way respectably. Obviously this Devi is not traditionally worshiped by many, so most of us do not know about her.
Vinayaki murty easily find in chausatha yogini temple of Hirapur, Bhubaneswar ,Odisha but it is ruined one .
The mythological and iconography of Elephant headed Goddess Vinayaki is not clear enough. Vinayaki the shkati of Ganesha matrika. She is worshiped in Ganesha Mantra. She is mounted in mouse . She is also regarded as the consort of Shri Ganesha. But we already know Ganesha has two wives like Ridhi and Sidhi. There is reason behind, Vinayaki is also known as the wive of Shri Ganesha just describe below.
Andhakasur the demon who has thousand of hands, two hundred eyes, arms and feet. Who had fight with Lord Shiva’s Male Army ( Shiva Gana )because he abduct Goddess Parvati. Andhak has some magical power, when drop of his blood touch the ground thousand of Andhakasur emerged . So it is much painful and difficult for shiva gana to win the fight with Andhakasura. Goddess Parvaty know every divine male entity has the attribute of male and female. So she is called of female energy from every male entity. For this way Indrani comes up from Lord Indra, Brahamni emerges from Brahma, Vaisnabi emerges from Vishnu and Vinyaki comes from Vinayak as half of female form so she is the consort of Ganapati. She is formed as warrior lady to fight with Andhakasur, other warrior Goddess is also jumped up to fight. There main objective to create obstacles to blood dropping on the ground. All of them success with objective,they are defeated the demon force Andhakasur. In Maschya Purana, Vishnu Dharamotar Purana and Bana Dugra Upanisad has clearly mention the female form of Ganesha, Vinayaki the fighter goddess. Vinayaki is also named as Gajanani, Ganeswari, Gajamukhi and Bighneswari.