Jim Learning, John Learning and Ken Mesher allegedly walked onto the site on Tuesday to protest an injunction to stay away from the area.
Jim Learning says the injunction infringes on his rights.
The three men made a brief appearance in court in Happy Valley-Goose Bay on Tuesday and are scheduled to return to court April 2.
Jim Learning says if found guilty, the men are facing a penalty of up two years in jail, or a $5,000 fine.
However, the member of the NunatuKavut Community Council says the energy corporation developing the site is the cause of the conflict, rather than the local people protesting at the site.
Learning says he and others hunted in the area when they were younger.
Gilbert Bennett, the vice president of the Lower Churchill Project, says in a news release that under the court injunction Nalcor is permitted to continue its site construction work without interruptions.
He says that the injunction says police "shall enforce the terms of this order," promptly.
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