Original Dravidian :
mother: aayi
Now found mostly among central Indian Dravidian tribes and Marathis and Konkanis. Among Marathis and Konkanis it could be Dravidian maternal lineages or Dravidian substrate. Its usage among some of the Kannada castes is due to Maratha influence in northern Karnataka region. Ironically, the term which was lost but reappeared because of non-Dravidian speakers.
So, the equivalent should be 'aaya' for father. Now observed only in Telugu as 'nayana'(my father).
Dravidian mixed with Harappan:
mother: amma, appa
father: appa, amma
Dravidian+Harappan mixed with Prakrits:
father: accha, ayya (equivalent to 'arya')
Others:
avva: most likely derived from 'amma'
akka, anna: result of consanguineous marriages