A Tamil asylum seeker family taken into custody a year ago during a dawn raid on their Queensland home will likely be deported after the High Court denied their final bid to stay in the country.

Nadesalingam, Priya and their two daughters have been in immigration detention in Victoria since March last year and had launched a case to avoid deportation back to Sri Lanka, where they claim they'll face persecution.

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In January, Home Affairs Minister Peter Dutton refused to grant the family a visa, despite the pleas of the tight-knit Queensland town of Biloela, where the family had settled.

The High Court of Australia on Tuesday refused Priya and Nadesalingam and their Australian-born daughters, Kopika and Tharunicaa, special leave to appeal last year's Federal Court ruling that they could not stay in the country.

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