Yep
In the south (TN, KA, AP, TE, KL) the first day is
Naraka Chaturdashi.
It celebrates Krishna slaying Narakasura (supposedly an evil king who used to torment his subjects)
In parts of KA, TN, AP, TE, KL the third day is also very significant.
Bali Padyami
It celebrates the short arrival of Mahabali to the earthly plane.
Story goes like this (short version):
Mahabali was a very benevolent and just king loved by his subjects. His only fault was 'ahankaar' or in english 'hubris'
Vamana (an avatar of Vishnu) taught him a lesson and pushed him to the netherworld or something.
Mahabali apparently asked for one favor. "Let me come to the earthly plane once a year to see how my subjects are doing"
On this day, Bali Padya, he apparently comes to this earthly plane during dusk for about 45 mins.
Incidently, in KL he also visits during Onam
Happy Deepavali!!
Feast with friends and family. Stay safe
Cheers,
Raghu