Christopher Brandon of Verona was convicted in 2009 of killing 15-month-old Xavier Staples in June of 2007. The baby was his girlfriend's son.
Authorities say Brandon had said at first that the baby had fallen from a bed. Two doctors and a pathologist testified the child's injuries were consistent with being violently shaken.
The Appeals Court on Tuesday rejected Brandon's claims prosecutors didn't prove he killed the child. The court says Brandon was alone with the child from 3 p.m. to midnight when he called 911 and a reasonable jury could conclude he killed the child.