Season 3 It can be assumed that Norman Osborn's life either was similar to the Ultimate Marvel version of the character, or somewhat resembles the show's version of the character. If his history resembles the show's version, it can be assumed that Goblin eventually further evolved from further doses of the Goblin Serum, which have mutated him even more into a winged, demonic Goblin.
When The Green Goblin goes after Miles' DNA, the power hungry Ultimate Goblin takes him on. When the Ultimate Goblin returns, he gives Miles a second chance to save (a version of) Peter. Peter gets battered around, and almost gives the Ultimate Goblin a chance to kill him. Miles saves the day by he using his Venom Blast (an electric attack only Miles possesses) to shock the Ultimate Goblin.
Season 4 Doctor Octopus teams up with Baron Mordo and uses the Siege Perilous to summon the Ultimate Green Goblin to recruit instead. When the demonic Goblin learns of the Siege Perilous' capabilities, he attempts to destroy all of reality with it, but is stopped by Spider-Man, Doctor Strange and Miles Morales, who uses his spider-sting to destroy the Siege Perilous, stranding him and his world's Goblin in the original universe. With no other options, at first the Ultimate Green Goblin first HYDRA attempt to make him a slave however, HYDRA is planning to recruit most of the dangerous villains like the Ultimate Goblin himself to destroy Spider-Man and his fellow Web Warriors, thus joining Doc Ock's Sinister Six.
Later, Doc Ock and the other members attacked the Triskelion. He fought Kid Arachnid and Dagger but was defeated by Kid Arachnid's stinger. But he recovered fast and defeated Kid Arachnid and blasted the wall on to Scarlet Spider. He fought Spider-Man again believing that it was his destiny to come to Spidey's universe. He was defeated this time when Spider-Man folded his wings around and knocking him against the wall.