The killer nurse had put forward four grounds of appeal, in each of which she claimed the judge wrongly refused an application made on her behalf during her trial.
Lucy Letby has been denied permission to appeal against her convictions for murdering seven babies and trying to kill six others.
Letby was sentenced to 14 whole-life orders in August after she was convicted of carrying out the offences at the Countess of Chester Hospital's neonatal unit, where she worked as a nurse, between June 2015 and June 2016.
In April this year, the 34-year-old renewed an application for leave to appeal in front of three judges at the Court of Appeal in London.
She put forward four grounds of appeal, in each of which she claimed the judge wrongly refused an application made on her behalf during her trial.
Letby, from Hereford, was found guilty of seven counts of murder and seven counts of attempted murder, two of which were against the same baby, and cleared of two further attempted murder charges after a 10-month trial at Manchester Crown Court.
The jury couldn't reach verdicts on six counts of attempted murder, relating to five children.
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