Puranas list a number of kings and dynasties that will rule after Mahabharata. It looks like different Puranas list different kings. So, what happened in the history after Mahabharata in India as per majority of the Puranas? Pandit Kota Venkatachalam just provided wrong information if you look at various Puranas. For example, he said Mauryas ruled for 316 years, while Puranas say they ruled for 137 years.
The query can be answered with reference to Srimad Bhagavatam. Canto XII Chapter I enumerates the dynasties and their kings. I give below the brief meaning without narrating words like son, brother, etc. I have also ignored the descriptions of the qualities and attributes of the kings as well as references to Kaliyuga and the declining morality and Dharmic qualities of the kings. I have covered verses 2 to 31, but by the 28th stanza I could not find corresponding English terms either in my vocabulary or in internet searches - any clarifications of such terms highlighted below would be most welcome and helpful to me too.
"As I have already clarified earlier in the Ninth Canto,in Jarasandha's lineage the last king will be Puranjaya. Puranjaya's Chief Minister Shunaka will assassinate him and install his own son Pradyota as the ruler of Maghada. Pradyota Dynasty will rule for 138 years. The kings will be Pradyota, Palaka, Vishakayoopa, Rajaka and Nandivardhana.
Thereafter Shishunaga Dynasty will rule for 360 years. The Kings will be Shishunaga, Kakavarna, Kshamadharma, Kshetragya, Vidhisara (Bimbisara), Ajatashatru, Dharbhaka, Ajaya, Nandivardhana (II) and Mahanandi.
Mahanandi also known as Mahapadma will be the last Kshatriya King. He will beget from his Shudra wife a son named Nanada who will succeed him. Nanda Dynaty will rule for 100 years and the rulers will be Nanda, Sumalya and his seven brothers.
Nanda dynasty will be destoyed by a Brahmin known variously as Chanakya or Kautilya whowill install the Maurya Dynasty on the throne. The Maurya Dynasty will rule for 137 years. The kings are Chandragupta, Varisara,Ashokavardhana, Suyasha, Sangata,Shalishooka,Somasharma Shatadhanva and Brihadhata. [As per Vishnu Purana Suyasha is succeeded by Dasharatha who in turn is succeeded by Sangata].
The commander - in - Chief of Brihadhata, Pushpamitra Shunga will assassinate him and install himself as the king. The Shunga Dynasty will rule for 112 years and its kings will be Pushpamitra, Agnimitra, Sujoyshreshta, Vasumitra, Pulinda, Ghosha, Vrajamitra, Bhagavata and Devabhuti.
Devabhuti will be assassinated by his minister Vasudeva Kanva who will install himsel the king. The Kanva Dynasty will rule for 345 years and the rulers will be Vasudeva, Bhoomimitra, Narayana and Susharma.
Bali, a Shudra servant of Susharma will assassinate him and succeed him. The Bali Dynasty will rule for 456 years and its kings will be Bali, Krishna, Shreesantha, Pornamaasa, Lambodara, Chiblik, Meghaswati, Atmana, Anishtakarma, Holaya, Talaka, Purishbhiroo, Sunandana, Chakra, Shivaswati and his eight brothers, Gomtiputra, Purimaana, Medhashira,Shivaskanda, Yagyashree, Vijaya, Chandrayagya and Lomadhi.
Thereafter, seven Abhir Kings, ten Gardhabhi Kings, sixteen Kanka Kings, eight Greek Kings, fourteen Turk Kings, ten Garunda Kings and eleven Mauna Kings. These kings other than Maunas will rule for 1099 years, while the eleven Mauna kings will for 306 years.
I have not gone into the remaining 12 verses describing the other kings of Kali Yuga. I hope, this answer is a satisfactory reply to your query.