He murdered his daughter in a fit of rage, but was never convicted of the crime. Wanting to undo that tragedy, he worked on creating a time machine so he could send someone back and save her. He needed a psychic to monitor the time traveller, so he spiked some water with a prototype cognition enhancer to jumpstart those abilities in people.
The drug succeeded with Josh Randall, but made him psychotic as a side effect. When the time machine was activated, it went out of control. Finer tried to turn it off, but Randall used his powers to kill him.
Fortunately, the Fourth Doctor and the TARDIS were able to control the machine. A new timeline was created, where Finer confessed to his daughter's murder. He never tried to build a time machine, and never drugged anyone to generate psychic powers. (PROSE: Psi-ence Fiction)