The Kings of Magadha - before the Great Mahabharata War - and - between Mahabharata War and beginning of Kali

The following list of Magadha kings is given according to Matsya Purana. As the reigning periods of the earlier Magadha kings (before the Mahabharata war) are not available in any one of the Puranas, the reigning periods of the earlier kings of Nepal are adopted for the Magadha kings as they were contemporary rulers with them.
Before the Great War ---- Barhadradha Dynasty:
From about 1058 before Kali(B.K.) or 1021 B.Y.(Before the coronation of Yudhistira) or 4159 B.C. to 36 B.K.(Before the commencement of Kaliyuga) or 3138 B. C.
( Total 1021 years )

After the Mahabharata War, 3138 B.C.,  36 years before Kali. 
19. Somapi or Somadhi( or Marjari) was crowned as king in Girivraja(capital of Magadha)..36 years Before Kali(B.K.)...reigned from 36 B.K.-to-22 A.K(After Kali) for 58 years, that is from 3138 to 3080 B.C.


Barhadradha Dynasty Before the Mahabharata War of 3138 B.C.
1. Barhardradha I :-
According to Mahabharata, Brihadradha-I, the founder of Barhadradha Dynasty was the eldest son of Uparichara Vasu , the seventh in the descent from the Great Kuru, son of Samvarna, a descendant of the Lunar Dynasty (Chandravamsajah) of kings. He founded the kingdom of Magadha probably about 3709 B.C. or 571 years before the Great war of Mahabharata at Kurukshetra between the Pandavas and the Kauravas.
This  battle according to Mahabharata, the important Puranas, and all other ancient Hindu, Bauddha and Jaina authorities and traditions, took place. 36 years before the commencement of the Kaliyuga—the present Yuga.   Kali Yuga  began immediately after the departure of Sri Krishna, son of Vasudeva by Devaki, from this world on the 20th February, 3102 B. C., in the year Pramadhin of the Southern School of Hindu astronomers. (Vide Indian Eras By this author, Kota Venkata Chelam)
Brihadradha married the two beautiful twin daughters of the king of Kasi; and by the blessing of a Rishi, he obtained a most powerful son by name Jarasandha. The king, after installing his mighty son Jarasandha on the throne of Magadha retired into a forest and led an ascetic life. In this context the Mahabharata gave the next prominent dynasty of Jarasandha, leaving some generations of kings in the interval between Brihadradha I and Jarasandha (or Brihadradha II). - (Vide_Mahabharata, Sabha Parva. Adhyayas 14 to 19).
N.B:- The Matsya Purana enumerates all the names of kings between Brihadradha-I and Jarasandha or Brihadradha-II Jarasandha, son of Bhuvana was the 15 th in descent from Kuru and the tenth from Brihadradha-I, the founder of the Magadha Dynasty of kings. The following table shows the order of descent according to Matsya Purana. (Chapter 59):-
1. Samvarna
2. Kuru (The founder of the Kaurava Dynasty who removed his capital from Prayaga to Kurukshetra.)
3. Sudhanvan, Parikshit, Prajana, Jaghnu or Johnu or Yaju
4. Suhotra.
5. Chyavana
6. Krimi (or Kriti)
7. Chaidya or Uparicharavasu or Pratipa
8. (1) Brihadradha-I thefounder of the Magadha Dynasty.(3709 B.C.)
9. (2) Kusaagra
10. (3) Vrishabha or Rishabha.
11· (4) Pushpavat or Punyavat
12. (5) Pushpa or Punya
13. (6) Satyadhrithi or Satyahita.
14. (7) Sudhnvan II or Dhanusha.
15. (8) Sarva
16. (9) Bhuvana or Sambhava.
I7. (10)Brihadradha II or Jarasandha.
18. (11)Sahadeva (Sahadeva died in the Maha-Bharata War)
According to this account, the commencement of the Barhadradha Dynasty of Magadha kings should be placed at about (571) B.Y.(Before the coronation of Yudhistira) or 3709 B.C.,allowing on an average at least 52 years for each king. i.e., The eleven kings from 8th to 18th King Sahadeva reigned Magadha from 3709 B.C. to 3138 B.C.