Aquaman is a bit of a busy guy, and as a result has three sons. Well... maybe.
Koryak is the son of Kako and Arthur. He was the result of a fling Arthur had as a teen when he visited Alaska and spent some time among the Inupiat there (Aquaman: Time & Tide #3). Arthur didn't know his visit resulted in a child until years later, when he returned to visit Kako (Aquaman #5 (Jan-95)). During Arthur's visit, Kako became a fire elemental. Because the Inupiat had never accepted Koryak anyway, he chose to go with Aquaman to Poseidonis. Koryak's has "hard water" powers that allow him to shape and control water, including making solid forms out of it.
Artie Jr was born to Mera and Arthur when Aquaman was king of Atlantis (Aquaman #23 (Oct-65)). He exhibited powers at an early age, leading to his banishment from the city for a short time. He never got to develop them fully though, as he was suffocated by Black Manta (Adventure #452 (Aug-77)).
Arthur Jr, aka "AJ", was born to Mera and Arthur... or maybe to Mera and Thanatos. It's hard to say for certain, as his birth occurred about nine months after Thanatos used his powers to drive Mera insane and pull her into a fantasy world in another dimension in which he played the role of Aquaman (Aquaman #14 (Nov-95)). Unfortunately, as soon as AJ emerged into the real Aquaman's world, he began to age rapidly and was only saved by another interdimensional trip. He later returned to ask for Aquaman's help (Aquaman #47 (Aug-98)) and in the end became the ruler of the other dimension.
Another candidate for Arthur's son would be Aqualad/Tempest/Garth. It's hard to say for sure what the relationship between Garth and Arthur is, as early in the Silver Age Aquaman was clearly a father figure for Garth but later stories show them acting as brothers to each other. Perhaps the Silver Age Aquaman was Garth's adoptive father, but the Post-Crisis relationship was almost certainly one of older brother/younger brother, with some strange forms of sibling rivalry going on in there. In any case, young Garth did feel jealous and worried when Artie Jr was born, as perhaps he should have been because Arthur was willing to kill Garth to protect Artie.
I suppose taken all together, these four kids add up to three sons...