The Assad government, which is led by the Muslim Alawite minority, has faced accusations of repopulation along sectarian lines.
In strategic areas across the country, Sunnis, who have largely supported the uprising against the regime, have been forced out.
One of the 28 included in the lawsuit told how they were forced to flee to Jordan, which is hosting more than 1.5 million Syrian refugees.
One woman, who requested anonymity because of a fear of reprisal, described how government forces targeted her family after her brother decided to leave the military. She testified about repeated raids on her family’s home in the middle of the night, threatening her family with death when they did not find him.
They fled from Syria to Jordan in late 2011.
Another, from the central Syrian city of Homs, said she became a target because of her work treating protesters in the early days of the conflict.