Sisko had been married to Sarah Sisko; unknown to him at the time, however, Sarah's body had been occupied by a Prophet to see that their Emissary was born. When the Prophet left Sarah a year after Benjamin was born, Sarah left as well. After her disappearance and ultimate death, Joseph Sisko remarried and had at least three other children with his new wife: Judith and at least two other boys. DS9: "Image in the Sand"
He would refer to his children as his "test tasters" as he would use them to try out new recipes. (DS9: "A Man Alone") Joseph was a master chef and owner of the restaurant Sisko's in New Orleans on Earth. He passed on his excellent cooking skills to Benjamin and Jake. (DS9: "Emissary", "Homefront", "Paradise Lost")
After the Dominion bombing at Antwerp, his son, grandson and Odo traveled to Earth. Shortly after, Starfleet authorities on Earth, with assistance from Benjamin Sisko and Odo, made it mandatory for the families of all Starfleet officers to undergo blood screenings. He resisted this, and complained that his freedoms were being usurped by the government. (DS9: "Homefront", "Paradise Lost")
In 2374, Joseph was very distraught to learn that Jake was the only Federation citizen to remain on Deep Space 9 following the Dominion occupation. He urged Ben to go rescue his son, though Ben reminded his father that during a time of war, that was not his choice to make. (DS9: "A Time to Stand")
Later that year, in spite of the Dominion War, he left Earth for the first time to visit his son and grandson on Deep Space 9. During his visit, Benjamin was sent a vision by the Prophets in which Joseph took the role of a 1950s preacher. (DS9: "Far Beyond the Stars")
When Ben left his post on Deep Space 9 following the murder of Jadzia Dax and the disappearance of the Bajoran wormhole, he moved into his father's home. It was here that Ben had visions of a Sarah Sisko. Although refusing to do so at first, Joseph would explain that Sarah was Ben's real mother who left after his birth. Joseph then accompanied his son to Tyree in search of answers as to who Sarah really was and to find the Orb of the Emissary that would release the prophets and re-activate the Wormhole. (DS9: "Image in the Sand", "Shadows and Symbols")
Joseph Sisko was first mentioned by Benjamin in DS9's premiere episode, "Emissary", in the past tense with the statement "My father was a gourmet chef." Both this and Benjamin's recounting of his grave illness in "The Alternate" suggested the elder Sisko was deceased at that point, before "Homefront" revealed him to be alive, if not in the best of health, an element which may have been a nod to "The Alternate"
The line in "Emissary" may also be interpreted as Joseph having given up cooking at some point before opening Sisko's Creole Kitchen, or it may have been that details of the Joseph Sisko character had simply not yet been developed.
Notably, Joseph is the only parent of the captain on any Star Trek series to be featured alive during the show's run. Nothing was revealed of the fathers of Christopher Pike or James T. Kirk during the run of the original series (though, many years later, the film Star Trek would state that Kirk's father George lived at least long enough to see his son take command of the USS Enterprise), while the fathers of Jonathan Archer (Henry Archer), Jean-Luc Picard (Maurice Picard), and Kathryn Janeway (Admiral Janeway} were explicitly said to have died many years before their respective series began. None of the above captains' mothers appeared both alive and on-screen. (The parents of several First Officers and other senior staff, however, did appear, most notably Spock's parents, Riker's father, Worf's adoptive parents, Counselor Troi's mother, and T'Pol's mother.)
Joseph dies of complications caused by pre-existing health problems in 2381, in the novel Rough Beasts of Empire.