Inzamam scored 329 in what became a 1-match series due to the later matches being cancelled (Pakistan v NZ 2002).Though sometimes players played less than a full series we have these records
Most runs in X match series
6 - 839 Taylor 1989 Ashes
5 - 974 Bradman 1930 Ashes
4 - 769 Smith 2014/15 B/G Trophy
3 - 752 Gooch 1989 India vs England
2 - 571 Jayasuriya 1997 India vs Sri Lanka
The numbers could possibly be off for the 2 test series, I had to make the cutoff before the first WTC since it was endless scrolling through those records on statsguru. Unsure of the highest score in a one-off test.
Najmal Hossain Shanto scored 270 for Bangladesh v Afghanistan in their Test last year.