Some TMNT stuff really isn't for little kids.
Dr. Baxter Stockman is a scientist at TCRI in New York City. He is a minor character in the 2014 live-action movie played by K. Todd Freeman, and had a bigger supporting role in the 2016 sequel, this time played by Tyler Perry.
Teenage Mutant Ninja Turtles
He only makes a quick cameo when young April O'Neil asks Eric Sacks what the experiments were for. In the scene, we see Sacks, April's dad, and Baxter Stockman standing in the background. In a later scene, Stockman's name was written on a whiteboard by April when she is trying to put together her knowledge of Project Renaissance.
Teenage Mutant Ninja Turtles: Out of the Shadows
April began shadowing Stockman a year later, believing that he was tied somehow to Shredder and the Foot. Her suspicions turned out to be correct, as Stockman was deeply involved in a plan to free Shredder from a prison convoy. As the Turtles attempted to recapture Shredder, Stockman used his untried teleporter to remove Shredder from the area.
Stockman was later consulted by Shredder in the use of the purple ooze, and in the reconstruction of the Arc Capacitor. He was deeply excited by the prospect of interdimensional travel and the power it would give them, predicting that other scientific geniuses would be "footnotes" beside him.
However, Stockman's arrogance and plans began to irritate Shredder, and after the activation of the Arc Capacitor, Shredder ordered Stockman to be taken to the Tokyo branch of the Foot Clan. Stockman resisted, but was dragged away into a Foot vehicle. His whereabouts are unknown at the story's end.