Sideman told the justices his client was asking that the conviction be removed and that a new trial be conducted.
Barfield, also found guilty of using a knife as part of the crimes, was sentenced to life in prison plus four years and eight months.
Barfield was arrested in October 1999 for the alleged attempted rape and attempted murder of a woman identified in court records as Evelyn P.
The records state Barfield was aquatinted with the victim and agreed to drive her to view a trailer the victim could rent.
Instead, Barfield reportedly drove to an area near the New River, stopped the car and attempted to sexually assault the woman.
Barfield then reportedly forced the woman and her children to the New River. Once there he reportedly cut her throat with a box cutter and threw large pieces of concrete on the victim and her children.
He eventually left the victims hiding in the highly polluted water.
Sideman argued before the justices that the prosecution's case against Barfield had been unfair and he claimed some jurors had a problem with the case. Barfield and his attorneys have argued the trial court erred in denying his motion for a mistrial.
One key point in his appeal was that the court allowed "hearsay" evidence in recorded testimony Evelyn P. had given to police while also allowing her to testify during the trial.
That "hearsay" testimony was allowed in when the prosecution had trouble locating her early in the trial.
The appellate court justices ruled Barfield's right to due process had not been violated and the trial court had not erred in denying the motion for a mistrial.
The justices said the fact that the woman was found and was able to testify allowed both the prosecution and defense to question her.
Sideman last week said if the appellate court sided against his client, the case could be presented to the state Supreme Court.
Staff Writer Darren Simon can be reached at 337-4082.