Araneus Oscorpeus is the species of genetically modified spiders created by Richard Parker. The modification involves a common household spider, radioactive isotope and compatible human DNA. Richard Parker's newly found discovery was going to save the lives of millions including Norman Osborn's.
However, Norman Osborn wished to use Richard Parker's research for biological weapons and did so by contacting a foreign military organization to continue funding his research. Richard Parker refused to continue his work for Oscorp and fled the country.
Norman Osborn framed Richard Parker, saying that he betrayed his best friend for the money would that be offered for his research. What Oscorp did not know was that Richard Parker used his own DNA to genetically modify the spiders, so without his bloodline Oscorp would be unable to continue the work for the biological weapons. Peter, Richard Parker's son, was bitten by one of these spiders, and it gave him his amazing spider-like abilities that allowed him to become Spider-Man.
After Curt Connors, a scientist working at Oscorp, tried to turn everyone in New York into lizard monsters, the spiders were killed to comply with lawsuits. Several vials of Araneus Oscorpeus venom were kept in the Special Projects division in the Oscorp building, one of which Green Goblin was injected with. The spider venom sped up the process of Harry's genetic disease (Retroviral Hypodisplasia) thus turning him into the Green Goblin. Harry crawls into a small alcove where the glider is located and gets onto it. The glider detects damage to Harry and the healing capability of the glider takes effect on him.
These spiders were genetically engineered by their creator Richard Parker to bite a person. Injecting a copy of their DNA instead of ordinary venom, which will give the human spider-like powers and traits. Richard intended for the spiders to help heal people from diseases and injury by passing the spider's healing factor and Immunity responses to humans, but Oscorp was going to weaponize it and create spider-soldiers for the highest bidder. After getting rid of Richard Parker, the venom from these spiders was extracted and placed in Oscorp's Special Projects division, along with the Vulture Wings, Dr. Octopus' Arms, the Rhino-Mech and the Green Goblin's Gear.