Final answer:
The detailed historical passages provided do not include specific information about a battle where the Dagbanis defeated local people, hence it is not possible to definitively answer the question based on the given text.
Step-by-step explanation:
The history of the Dagbanis, a people from the northern part of what is now Ghana, indicates a series of conflicts and victories over various local groups throughout history. However, the specific event where the Dagbanis defeated the local people is not detailed in the provided passages. The accounts mentioned speak of several historical conquests such as the Dutch colonization and consequences for the Bandanese (1621), the Mamluk victory over Mongols at the Battle of Ain Jalut (1260), the Sefuwa dynasty's consolidation over Bornu, the Saadi conquest of the Songhai Empire, and the decline of the Malian Empire due to external pressures and internal uprisings. The exact battle in which the Dagbanis defeated the local population isn't outlined in these passages. Therefore, without specific historical records related to the Dagbanis that detail such a battle, it is not possible to definitively answer the question.