Such as the Sherlock Holmes novels or Baum’s Oz books. Who was the first author to make a career out of churning out a series of books about the ongoing adventures of a character or set of characters?
There was a series of Nick Carter dime novels starting a year before Sherlock Holmes saw print.
Ned Buntline wrote a series of novels in the 1830s, but I’m not sure if he used the same characters in each.
Certainly sequels existed pretty early: Alexander Dumas wrote sequels to The Three Musketeers, the first in 1845.
C. August Dupin showed up in Edgar Allen Poe stories starting in 1841.
Rabelais wrote the Gargantua & Pantagruel books in the 16th century.
Cervantes came up with a sequel to Don Quixote in 1615.
Well, the Odyssey picks up the story of one of the characters in the Illiad. Neither were books, both were expanding on stories already in place in a mythic tradition and the main characters are different, so I guess you can debate whether that counts or not.