Razwan Ali Anjum was handed a fourth consecutive jail term by a High Court judge in April after he refused to reveal where his daughter was.
Mr Justice Moor imposed a 12-month prison sentence after he found him in contempt of a High Court order instructing him to disclose her whereabouts.
He said Anjum, who is in his late 20s, would not be eligible for release until he had served at least six months.
Judges have previously imposed jail terms of two years, 12 months and another 12 months in the hope that Anjum would provide information.
They have re-jailed Anjum as each sentence neared its end.
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