Lucy Letby's lawyer Mark McDonald announced he will seek permission to apply to reopen the appeal and review all her convictions.
A key prosecution witness, Dr Dewi Evans, had changed his mind on the cause of the deaths of three babies, referred to as C, I and P, Mr McDonald said.
Dr Evans was no longer a reliable witness because he gave "one theory" to the jury and has not stood by it, claimed Mr McDonald.
He also read out a statement by two consultant neonatologists that said they found "no evidence of deliberate harm" to babies C and O after reviewing Dr Evans' reports as well as hospital notes, postmortem and witness statements.
Baby O died "due to issues relating to the resuscitation" and Baby C died due to "problems caused due to failing placental function at the end of the pregnancy", the statement read.
Mr McDonald compared Letby to the victims of the Post Office scandal, in which hundreds of sub-postmasters who used faulty Horizon IT software were wrongly convicted for theft, fraud and false accounting.
Medical expert Dr Richard Taylor told reporters Baby O died after they were put in an inappropriately high-pressure ventilator, which pushed their liver into the pelvis.
Separately, a doctor inserted a needle into the baby's distended abdomen on the right side to aspirate it, lacerating the liver and sending the baby into shock, he claimed.
He said he believed Lucy Letby, like all nurses, wanted to help other people.