Trogyllium is a rocky area in the sea between the island of Samos and the city of Miletus. In Acts 20:15, some early copies of the Bible mention that Paul's ship stopped at this place during his journey to Jerusalem near the end of his third missionary journey. Since Trogyllium is a piece of land that sticks out into the sea between Samos and Miletus, it would be reasonable for a sailing ship to have stopped there for the night.
However, most scholars who study ancient Bible manuscripts believe the phrase "after remaining at Trogyllium" (which appears in the King James Version) was added to the Bible text later and was not part of the original writing.