Vadadra are the followers of Bala Mata, a form of Amba Maa with eighteen hands. They are Brahmins who are named after the village Vadad or Valad (other names are - Vadadras, Valadras, Varadra, Valadhra or Valandra), near to Ahmedabad. The name of the town Vadad was adopted by the community living around the temple of Bala Mata. They are Devi Bhakts.
References
Vadadra Brahmin Wikipedia(Text) CC BY-SA