While her gemstone and name are not mentioned on-screen, the fusion's design was confirmed by Rebecca Sugar to be inspired by the gemstone Zebra Jasper.
Zebra Jasper has dark orange-yellow skin with mahogany patches caused by the Snow Monster's corruption. Her hair is off-white, and extends down to her midriff. She has a tail of the same hair. Her body is monstrous, having four arms and four wolf-like legs. Her face is taken from Jasper, but with the Snow Monster's mouth. She has five horns on her head, three of which extend out and up. The other two resemble ram's horns extending down. She is approximately two and a half times Jasper's size when on six legs, and about three and a half times Jasper's size from head to tail.
Not much is known about Zebra Jasper's personality, but she is very aggressive, her immediate response to fusion being to simple-mindedly attack Smoky Quartz. She appears to have a lack of strategy or complicated thinking, as her only method of fighting Smoky is to lumber towards them and swing, which she continues to do even when being blown back by Smoky's yo-yos.
During her fight with Smoky Quartz, Jasper decided to fuse with the Snow Monster in a desperate attempt to turn the tide of battle. This resulted in the creation of Zebra Jasper, who did not take long before she started to attack Smoky with some swift slashes from her clawed hands.
However, despite scaring the fusion at first, Smoky quickly regained the upper hand by using their yo-yos to "blow her away". Zebra Jasper, despite being caught off-guard by the attack, managed to withstand it and slowly advanced toward to Smoky, ready to attack.
Unfortunately for her, Smoky simply summoned more yo-yos to create a tornado, which in return caused the fusion to rise into the air and defuse. Jasper tried to force the Snow Monster to remain fused, but the monster overwhelmed her and ran away when given the chance, leaving Jasper to be corrupted because of the fusion.
Zebra Jasper was later referenced in "Know Your Fusion" by Smoky while they were talking with Sardonyx in her room, where they said Jasper had a "short fuse" before being corrupted.
It is unknown if Zebra Jasper can speak, as her few utterances have been animal-like growls, cries, and one laugh, presumably from Jasper.
Zebra Jasper is the first fusion between a normal Gem and a Corrupted Gem, as well as the first fusion involving a Corrupted Gem in general.
After unfusing, Jasper became corrupted as well, slowly degenerating into a similar Gem monster – notably, the corruption matched the Corrupted Gem's color palette, not Jasper's (showing that a Gem can be corrupted just by fusing with a Corrupted Gem), although greenish impurities are somewhat common in real-world quartz.
Although the Snow Monster's gemstone is a hexagon, it is shown to be round while fused. This was most likely an animation error.
Just like Malachite, Zebra Jasper has a centaur-like body shape.
Rebecca Sugar mentioned on The Best Show that the fusion is actually based off of yellowish varieties of Zebra Jasper, but that she doesn't (yet) have that name.
Jasper's gemstone is located where the fusion's nose would otherwise be. It is triangular, and faceted onto a low point. It has a diamond-esque shape.
The Snow Monster's gemstone is on her chest, similar to Amethyst's gem's placement. The gem is hexagonal.
↑ 1.01.11.21.3The Best Show
1:44:00 - "The fusion isn't called Tiger's Eye, but it's indeed a type of Jasper."
1:49:00 - "The fusion is based off a specific type of Zebra Jasper. Some Zebra Jaspers are tinged a little orange. She wouldn't call herself that yet, because she has to decide on her own name, but most likely she would call herself that."