Did the Ostrogoth establish a kingdom in Spain?

Yes, the Ostrogoths did indeed establish a kingdom in Spain. During the 5th century A.D., the Visigoths, who were a Germanic people closely related to the Ostrogoths, established the Visigothic Kingdom in the Iberian Peninsula, which included most of modern-day Spain and Portugal. The Visigoths ruled over Spain for several centuries, and they played a significant role in shaping the political, cultural, and religious landscape of the region.