The Federation Immigration was a department in the Federation that handled matters of immigration.
In 2352, after Darryl Adin rescued Tasha Yar from New Paris (Turkana IV) and took her to Earth, Federation Immigration remembered that the world had formally seceded from the Federation, and thus decided that taking her away had been illegal. They wished to send her back to the dystopian world, and the matter came to a legal case. Fortunately, the most powerful drug-lord on New Paris, its de facto spokesman, said that no-one wanted her and offered the rest of the world's homeless, orphaned children. The matter was dropped and Yar was allowed to stay on Earth. (TNG novel: Survivors)