What castle did William order built at Dover after the battle?

The castle William ordered built at Dover was Dover Castle. However, the question's timing needs care: William ordered the first fortification at Dover shortly after landing in England, before the Battle of Hastings, and later strengthened it after his victory.

Dover was strategically vital because it guarded the shortest sea route between England and Normandy. William's army passed through the area during its march toward London after Hastings, and a castle there helped secure the port, the road network, and the Channel crossing.

The earliest Norman structure was a wooden motte-and-bailey fortification. The massive stone castle visitors recognise today belongs mainly to later rebuilding, especially during the reign of Henry II in the twelfth century. That distinction explains why the castle is often associated with William even though much of its surviving architecture is later.

Dover is sometimes confused with Pevensey or Hastings castles, both of which William also ordered built during the invasion. Windsor Castle was part of a later defensive strategy around London, while the Tower of London was developed after the conquest. Dover became known as the “Key to England” because of its defensive and maritime importance.