(covers information from several alternate timelines)
"And he makes a fierce jambalaya."
Joseph Sisko was the father of Starfleet captain Benjamin Sisko and Judith Sisko and grandfather of Jake Sisko. He lived in the city of New Orleans on Earth was the owner and master chef of the Creole food restaurant Sisko's Creole Kitchen.
In June 2331, Joseph Sisko fell in love with a woman named Sarah; unknown to him at the time, however, Sarah's body had been occupied by a Prophet to see that their Emissary was born. Two months later, he married her and they had their child, Benjamin. Shortly after Benjamin's birth, Joseph was known to show off the newborn in one arm, while serving tables with the other. However, when the Prophet left Sarah, Sarah, too left Joseph and Ben after his first birthday. After her disappearance and ultimate death in a hovercraft accident in 2336, Joseph decided not to tell his son about her and later remarried and had at least three other children with his new wife: Judith and at least two other boys. (DS9: "Image in the Sand")
Joseph grew his own vegetables and sent his sons out to the garden to harvest them. (DS9: "Paradise") 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 Creole Kitchen in New Orleans on Earth. He passed on his excellent cooking skills to Benjamin and Jake. (DS9: "Emissary", "Homefront", "Paradise Lost")
After the Dominion bombed the Antwerp Conference in 2372, 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 and that Jake was a grown man who could make his own decisions. (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")
Following the murder of Jadzia Dax and the disappearance of the Bajoran wormhole, Benjamin was despondent and grief-stricken over the loss of his friend. Consequently, he moved into his father's home and took to assisting his father in the running of his restaurant. It was here that Ben had visions of a Sarah Sisko. Although he was upset at first, refusing to discuss or acknowledge the identity of the woman Benjamin had seen visions of and subsequently completed a rendering of, Joseph would explain that Sarah was Ben's real mother who left after his birth. Joseph then accompanied his son to the planet 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.
In the Star Trek: Typhon Pact novel Rough Beasts of Empire, Joseph died in 2381 shortly after the Borg invasion of that year due to complications caused by pre-existing health problems. He was cremated and buried at Katrina Memorial Cemetery in his native New Orleans.