I was looking at Wikipedia page for India's major political parties and realized, almost all well recognized parties have strong nepotism and fiefdom of some family or individual. Here is the list, but feel free to correct or add more details.

Parties with a family's fiefdom

• Indian National Congress (Nehru and family)
• Samajwadi Party (Mulayam Singh Yadav and family)
• Janta Dal (Lalu Yadav and sons)
• Dravida Munnetra Kazhagam (Karunanidhi and family)
• All India Majlis-e-Ittehadul Muslimeen (Owaisi and sons)
• Jammu & Kashmir National Conference (Sheikh Abdullah and sons)
• Janta Dal (Secular) (HD Devegowda and sons)
• Lok Janshakti Party (Ram Vilas Paswan and son)
• Shiv Sena (Bal Thackrey and sons)
• Biju Janta Dal (Biju Patnaik and son)
• Telugu Desam Party (Chandra Babu Naidu and family)
• Telangana Rashtra Samithi (KCR and sons)
• Indian National Lokdal (Om Prakash Chautala and sons)
• Shiromani Akali Dal (Sukhbir Singh Badal and sons)

Supremo based parties

• Bahujan Samaj Party (Mayavati)
• Janta Dal (United) (Nitish Kumar)
• Rashtriya Lok Dal (Ajit Singh)
• All India Trinamool Congress (Mamta Bannerjee)
• AIADMK (Was fiefdom of Jayalalitha, but now unclear if party will be more democratic or if it will continue to exist)

Supremo based party list is debatable but for sure BSP and RLD are such parties. Finally, this leaves us primarily with following parties -

• AAP (Strong single leadership but party will not be in shambles without him)
• BJP (Strong single leadership but party will not be in shambles without him. Also multiple leaders have sons and daughters in party too but so far no fiefdom at party level.)
• CPI (It appears to be only major party free of nepotism or fiefdoms.)

Edit: modified w.r.t. TRS, TDP and also Didi's Trinamoola Edit2: added INLD and SAD