Gemma Wilkinson, a former charity worker, took legal action in an attempt to force Anjum to reveal the whereabouts of her daughter Atiya.
Anjum, who represented himself at the latest court hearing, indicated that Atiya was in Pakistan or Iran but said he did not know her exact whereabouts.
Mr Justice Moor said he was sure Anjum was lying.
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Paul Golding was arrested by police in Belfast earlier on Thursday while he was at court supporting deputy leader Jayda Fransen.