Carl Alesbrook, now 19, was unanimously convicted of murdering Elijah Shemwell, his partner's son, in January 2022 when he was left alone with the infant.
He was also found guilty of two counts of causing grievous bodily harm, relating to attacks on Elijah that caused bleeding on the brain, whiplash-type injuries and multiple bone fractures.
The trial at Derby crown court heard that Elijah was shaken on three separate occasions, and died at Queen's medical centre in Nottingham on 5 January 2022 after going into cardiac arrest.
Alesbrook had met the baby's mother, India Shemwell, who was 21 at the time, seven weeks before the infant's murder and the pair began a relationship.
Shemwell admitted to two counts of child cruelty, including the fact that she did not telephone the emergency services more quickly after Elijah became unwell.
The prosecutor, Vanessa Marshall KC, said Alesbrook killed Elijah when he was left alone with the infant at Shemwell's home in Belper, Derbyshire.
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