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Mr. Adar said the three often travel, and — because J. is black, and they are white — an airline worker once stopped them, thinking that they were kidnapping the child. “Every time we fly, we fear this could happen again,” he wrote.

J. was born about eight weeks prematurely in Shreveport, La., in late 2005. He spent his first month in the hospital, and weighed 5 pounds when his mother gave him to Mr. Adar and Mr. Smith that December, according to Mr. Adar’s statement. The adoption was made final April 27, 2006, their lawsuit states.