If you ever wondered why Sega never bothered to make a new mainline Sonic the Hedgehog game for the entire lifespan of the Sega Saturn, then the answer is that they did. Okay, well, they tried to make one anyway. They just hit a few snags along the way. A lot of snags.
Originally intended for the Sega Genesis 32X add-on under the codename Sonic Mars, but moving over to the upcoming console during production, Sonic X-treme was a Platform Game developed by Sega Technical Institute. Intended to be the franchise's big transition from 2D to 3D gameplay, the game began production in late 1994 before being unceremoniously cancelled in 1997.
Following the completion of Sonic & Knuckles, series co-creator Yuji Naka and all the Japanese staff at Sega Technical Institute went back to Japan, while all the other members remained in the United States. While the Japanese Sonic Team was off making NiGHTS into Dreams..., the American crew was given the task to make a new mainline Sonic game.
What exactly this new Sonic game would entail on the story side of things changed quite a bit throughout development. It was originally conceived as taking place in the same continuity as the 90s Saturday Morning cartoon and the comic book series, sharing the same basic plot and characters. Sega would veto this idea, and the team would go on to give their game several different plot proposals even into its final year of development. This included everything from a story where Sonic had to stop demons that were trapped in the Master Emerald to one where our hero is just trying to get to a date with new character and Love Interest Tiara Boobowski on time. Many of these plots also involved having multiple playable characters, such as Tails and Kunckles, in addition to the aforementioned Tiara. But as the production shifted to the Saturn, it was decided that Sonic would be the sole playable character in order to keep things simple.
Sonic X-Treme was meant to have two different gameplay styles. Standard levels would have a fisheye camera known as the "Reflex Lens" that made levels appear as though they were moving around Sonic. Levels would also rotate around a fixed center of gravity as though they were small planetoids, allowing Sonic could run up walls and ceilings.note Meanwhile, boss stages were more free-roaming levels, with the boss fights themselves having the camera centered on the enemy in the middle and Sonic running around them in an arena.
So what lead to the game's cancellation? Basically, the game started with two development teams (Team A and Team B) that dealt with normal levels and boss levels, respectively. Team A's engine for the normal levels ran great on computers, but struggled on the Sega Saturn's hardware. While they managed to get it working decently well after some time, the ones who could demonstrate this version were just seconds late to a meeting held with CEO Hayao Nakayama in March '96, who ended up seeing an earlier poorly-running version and demanded that all of that work be scrapped and the whole game done in the style of the boss stages instead. And to get the game done by Christmas to compete with Super Mario 64. Depending on who you ask, Team B's attempts to make this happen either had them use the engine for NiGHTS or create content that looked very similar to that game: regardless, Yuki Naka saw this version of the game and threatened to quit Sega if it wasn't scrapped. The stress of having to now start from scratch to complete a game in just a few months had the head of the project contract pneumonia. Told that he would only have six months to live if he kept working at his current pace, he had to leave the project and the game as a whole was cancelled, as it would no longer release by the holiday season. With no 3D Sonic to speak of, Sega decided to port over Sonic 3D: Flickies' Island in its stead, and the blue hedgehog wouldn't see his first true 3D adventure for another two years.
For more detail on the game's development, see the three-part video series by Youtuber miiyouandmii2. Oh, and as a sidenote, this game was at one point meant as a tie-in for a proposed live-action film called Sonic the Hedgehog: Wonders of the World. The plot of this movie would have involved Sonic and Robotnik escaping from Sonic X-treme into the real world.