In my Medieval world there are two vast continents. The first of them is similar to Eurasia spreading from East to West, and the second is like Africa but not so arid. The shape of the Southern continent may not be the same too. Instead of the Mediterranean Sea and the Red Sea, the two continents are separated by a large ocean and there is a small archipelago sitting in the middle between them.
Is it possible this small island nation to control all the trade between the two continents? Could they be so far apart that it is impossible to travel between them without visiting the islands for supplies? Is it possible the fleet to prevent any attempt by traders to continue their journey to the north or south? Is it possible the costs of such a journey to be so high that traders will prefer to unload all cargo, sell it on the island's markets and go back to their homes? It will be even better if there are separate markets.
I am asking this because I want the populations of the two continents to know about each other as few as possible. They can exchange goods which are affordable enough for the ordinary person to consume them on regular basis. Most of the people are aware about the existence of the second land mass and have basic idea of its location but no one has ever seen it.
There is no magic and technology is at the level of the late Middle Ages.