For a reference, medieval kingdoms aside, there were 584 princely states in British India (idk if that means there were others outside British India). Also some states had different mints per city.
Since nobody probably even knows the name of all of them, I feel it's more practical to just cite the ones that have coins. I'll list all state names I can find anyway, while trying to cite/link to coins for each, so we know which have available coins:
Cita-Ajaighar, Princely State of
-Akalkot/Akkalkot, Princely State of
-Alipura, Princely State of
-Alirajpur/Rajpur, Princely State of
-Amb, Princely State of
-Ambliara, Princely State of
-Angadh, Princely State of
-Athgarh, Princely State of
-Athmallik, Princely State of
-Aundh, Princely State of
-Babariawad, Princely State of
-Baghal, Princely State of
-Baghat, Princely State of
-Balasinor, Princely State of
-Ballabhgarh, Princely State of
-Bamra/Bamanda, Princely State of
-Banganapalle, Princely State of
-Bansda, Princely State of
-Bantva Manavadar, Princely State of
-Baoni, Princely State of
-Baraundha, Princely State of
-Baria, Princely State of
-Barwani, Princely State of
-Basharh, Princely State of
-Basoda, Princely State of
-Bastar, Princely State of
-Baudh, Princely State of
-Beja, Princely State of
-Bela/Las Bela, Princely State of
-Benares/Banaras, Princely State of
-Bengal Presidency (not sure if that's the same as Bengal Sultanate)
-Beri, Princely State of
-Bhadranath, Princely State of
-Bhaisunda, Princely State of
-Bhajji, Princely State of
-Bhith-Bhagwanpur, Princely State of
-Bhopal-Narsingarh Feudatory
-Bhor, Princely State of
-Bijawar, Princely State of
-Bilaspur/Kahlur, Princely State of
-Bombay Presidency
-Bonai, Princely State of
-Changbhakar, Princely State of
-Charkhari, Princely State of
-Chhuikhadan, Princely State of
-Chitral, Princely State of
-Chuda, Princely State of
-Coorg, Kingdom of
-Danta, Princely State of
-Darkoti, Princely State of
-Daspalla, Princely State of
-Datarpur, Princely State of
-Dedhrota, Princely State of
-Dewas Junior, Princely State of (coin #19 in link)
-Dewas Senior, Princely State of (coin #20 in link)
-Dhami, Princely State of
-Dharampur, Princely State of
-Dhenkanal, Princely State of
-Dholpur, Kingdom of
-Dhrangadhra (Kuwa, Halad(-Dhrangadhra)), Princely State of
-Dhrol, Princely State of
-Dhurwai, Princely State of
-Dhir/Dir, Princely State of
-Faridkot, Princely State of
-Gangpur, Princely State of
-Gaurihar, Princely State of
-Gohad, Kingdom of
-Gondal, Princely State of
-Gorkha, Kingdom of
-Guler, Princely State of
-Guna, Princely State of (coin #24 in link)
-Hansi, Princely State of
-Hindol, Princely State of
-Hunza/Kanjut, Princely State of (also of Pakistan 1947-1974)
-Hyderabad-Aurangabad Feudatory
-Hyderabad-Firoznagar Feudatory
-Hyderabad-Gadwal Feudatory
-Hyderabad-Imamnagar Feudatory
-Hyderabad-Kalayani Feudatory
-Hyderabad-Narayanpett Feudatory
-Hyderabad-Shorapur Feudatory
-Hyderabad-Wanparti Feudatory
-Idar/Edar, Princely State of
-Jafarabad, Princely State of
-Jaintia, Kingdom of
-Jaipur-Khetri Feudatory
-Jaitpur, Princely State of
-Jalaun, Princely State of
-Jambughoda/Narukot/Tokalpur, Princely State of
-Jamkhandi, Princely State of
-Jammu, Princely State of
-Jandol, Princely State of
-Jaoli/Javli, Principality of
-Jashpur, Princely State of
-Jaso/Jassu/Yashogarh, Princely State of
-Jath, Princely State of
-Jawhar, Princely State of
-Jesar, Princely State of
-Jeypore, Kingdom of
-Jhansi, Princely State of
-Jigni, Princely State of
-Jind, Kingdom of
-Jobat, Princely State of
-Jubbal, Princely State of
-Kachar, Kingdom of
-Kaithal, Princely State of
-Kalahandi/Karond, Princely State of
-Kalsia, Princely State of
-Kamta-Rajaula, Princely State of
-Kanker, Princely State of
-Kapurthala, Princely State of
-Kawardha, Princely State of
-Keonjhar, Princely State of
-Keonthal, Princely State of
-Khairagarh, Princely State of
-Khairpur, Princely State of
-Khandpara, Princely State of
-Khaniadhana, Princely State of
-Kharan, Princely State of
-Kharsawan/Kharsua, Princely State of
-Khayrpur, Princely State of
-Khilchipur, Princely State of
-Khirasra, Princely State
-Kolaba, Princely State of
-Kolhapur-Kapshi, Princely State of
-Koriya/Korea, Princely State of
-Kothariah, Princely State of
-Kothi, Princely State of
-Kulpahar, Princely State of
-Kumarsan/Kumharsain, Princely State of
-Kurundvad Junior, Princely State of
-Kurundvad Senior, Princely State of
-Kuthar, Princely State of
-Kutlehar, Princely State of
-Ladakh, Kingdom of
-Lakhtar, Princely State of
-Lathi, Princely State of
-Lawa Thikana, Princely State of
-Limbda, Princely State of
-Limbdi, Princely State of
-Loharu, Princely State of
-Madras Presidency
-Maihar, Princely State of
-Makran, Princely State of
-Malpur, Princely State of
-Manda, Princely State of
-Mandi, Princely State of
-Maurha, Princely State of
-Mayurbhanj, Princely State of
-Mewar-Bhilwara, City of [Local Issues]
-Mewar-Bhinda Feudatory
-Mewar-Chitor, City of [Local Issues]
-Mewar-Jawad, District of [Local Issues]
-Mewar-Salumba Feudatory
-Mewar-Shahpur Feudatory
-Mewar-Umarda, City of [Local Issues]
-Miraj Junior, Princely State of
-Miraj Senior, Princely State of
-Mohammadgarh, Princely State of
-Mohanpur, Princely State of
-Morvi/Morvee/Morbi, Princely State of
-Mudhol, Princely State of
-Muli, Princely State of
-Mundru, Princely State of
-Nabha, Princely State of
-Nagar, Princely State of
-Nagas of Padmavati Dynasty (3rd-4th century)
-Nagod, Princely State of
-Nagpur, Kingdom of
-Nandgaon, Princely State of
-Narsinghgarh, Princely State of
-Narsinghpur, Princely State of
-Nasvadi, Princely State of
-Nayagarh, Princely State of
-Nazargunj, Princely State of
-Nilgiri, Princely State of
-Pahra, Princely State of
-Pal Lahara, Princely State of
-Palanpur, Princely State of
-Paldeo, Princely State of
-Palitana, Princely State of
-Patan, Princely State of
-Pataudi, Princely State of
-Patdi, Princely State of
-Pathari, Princely State of
-Patna, Princely State of
-Pethapur, Princely State of
-Phaltan, Princely State of
-Phulra, Princely State of
-Piploda, Princely State of
-Punial, Princely State of
-Raghogarh/Kichiwara, Princely State of
-Raigarh, Princely State of
-Rairakhol, Princely State of
-Rajkot, Princely State of
-Rajoli Zamindari, Princely State of
-Rajpara, Princely State of
-Rajpipla, Princely State of
-Rajpur, Princely State of
-Rajput-Jasrota, Dynasty of
-Ramdurg, Princely State of
-Ranasan, Princely State of
-Ranpur, Princely State of
-Sachin, Princely State of
-Sailana-Barmawal Feudatory
-Sakti, Princely State of
-Sambalpur/Hirakhand, Princely State of
-Samthar, Princely State of
-Sandur, Princely State of
-Sangli, Princely State of
-Santrampur/Sant, Princely State of
-Saraikela, Princely State of
-Sarangarh, Princely State of
-Sardargardh Bantva, Princely State of
-Satara, Princely State of
-Savanur, Nawabdom of
-Sawantwadi, Princely State of
-Selam, Princely State of
-Shahpura, Princely State of
-Siba, Princely State of
-Sikkim, Kingdom of
-Sirmur/Nahan, Kingdom of
-Sirohi, Princely State of
-Sohawal, Princely State of
-Somna, Princely State of
-Sonepur, Princely State of
-Sudasna, Princely State
-Suket, Princely State of
-Surat, Princely State of
-Surgana, Princely State of
-Surguja, Princely State of
-Swat, Princely State of
-Talcher, Princely State of
-Taraon/Tarahwan/Tarahuhan, Princely State of
-Tekari, Princely State of
-Thanesar, Princely State of
-Tigiria, Princely State of
-Torawati, Princely State of
-Tori Fatehpur, Princely State of
-Tulsipur, Kingdom of
-Vailavpur, Princely State of
-Vala/Vallabhipura, Princely State of
-Varsoda, Princely State of
-Vijaynagar/Pol, Princely State of (not the empire)
-Vijaipur, Princely State of
-Wadagam, Princely State of
-Wadhwan, Princely State of
-Wankaner/Vankaner, Princely State of
-Yasin/Worshigum, Princely State of
MINTS
-Kunch mint of Maratha Empire (I checked, not at numista) - Source
I hope I'm being helpful here. ANY corrections are welcome, like different names or if it was some jurisdiction or city and not an actual state with its own coins. I would put coin descriptions for each if that's necessary for them to be in the catalogue (should there be agreement on that about this list).
I'll keep updating this list.
Other Notes
-Bharuch=Broach
-Junagadh=Junagarh
-Mewar-Bhilwara/Chitor/Jawad/Umarda should probably go alongside Mewar coins as, e.g.
½ Paisa - Umarda (18XX-19XX)
-Oudh=Awadh
-Sant/Santrampur/Sunth/Sounth is under Rampur
-Thanjavur-Maratha, Kingdom of = Tore/Tori (wiki:
Doctrine of Lapse)
-Udaipur=Mewar
-Vala=Arcot
-Jammu has its own coins even though it was the princely state of Jammu and Kashmir (it was also a kingdom/state since 900)
Sources
-
https://en.wikipedia.org/wiki/List_of_princely_states_of_British_India_(alphabetical)
-
https://en.wikipedia.org/wiki/Category:Princely_states_of_India
-
http://www.coinindia.com
-
https://www.numisbids.com/n.php?p=sale&sid=2691&cid=74704
"Perfection can be achieved only through devotion" - Chanakya Nitishastra 8.10
"And fortune learnt to know her favorite" - Tacitus Agricola 13