The federal government has been ordered to pay a Tamil family more than $200,000 in legal fees over their bid to stay in Australia.

Priya and Nadesalingam and their Australian-born daughters Kopika and Tharunicaa, aged four and two, have spent more than two years in detention fighting their deportation to Sri Lanka.

Priya and Nadesalingam and their Australian-born daughters Kopika and Tharunicaa. Credit:Twitter/HometoBilo

Federal Court Justice Mark Moshinsky ordered the family's costs of $206,934 be paid, after they successfully argued their youngest daughter was denied procedural fairness in an application for a protection visa.

Immigration Minister David Coleman lifted a barrier to allow him to consider a visa application for Tharunicaa last May, but no decision was made.