I have not seen ospreys fishing over ocean waters, and perhaps these are not its prefered hunting grounds, but accounts from the 19th century often describe the birds over the sea. Ospreys are strong fliers capable of crossing the Mediterranean Sea and the Sahara Desert. They don't build up large fat stores to help sustain them on migration, instead hunting as they go. Most Northern Hemisphere ospreys migrate south in the fall. North American birds winter in Florida, the Caribbean, on the Gulf Coast, and even to South America.
European birds go to African coasts, lakes and rivers, mostly south of the Sahara.
Some birds in Florida, the Carribean, Australia, and around the Mediterranean do not migrate. Ospreys typically head south in September-October, and begin leaving the wintering grounds in early March. Breeding pairs are usually on the nest by mid March in more southerly parts of their breeding range and late April farther to the north. Ospreys will take advantage of just about anything affording a view of the water to build their nests, including tall trees, cliffs, buoys, telephone poles, the sides of bridges, and even wrecked ships. The bulky nest is constructed of rough sticks.