I think it must have been in Analog or Asimov in the early 1980s (81, 82, 83). It's a short story with only TWO characters: The prisoner and the psychiatrist.
A man is seeing the prison psychiatrist. During the session, he identifies the cruel treatment by his father as the root of all his problems. When back in his cell he time travels (this seems to be an innate ability he has - no explanation is given, as I remember) and kills his father.
The following day he is back with the psychiatrist and identifies his being brought up by a neglectful single-parent mother as the root of all his problems. Once again, back in his cell he travels back in time and kills her.
The following day he identifies a cruel carer at the orphanage he grew up in...
The story goes through a number of, Groundhog Day style loops and finishes with a clever dark twist.
After a number of loops - all the possible people who may have influenced him in a bad way killed it ends with him in the psychiatrist office thinking,
'maybe seeing this psychiatrist has caused me to be the way I am?!' - Leading the reader to believe he will travel back in time and kill the psychiatrist before their first meeting).
