Atsinna was a pueblo built in a defensive position atop Inscription Rock at what is now El Morro National Monument. The pueblo was only occupied for about 75 years, from about 1275 to about 1350 CE. That was a time of greater warmth and wetness, a time of expansion for the Zuni people and they moved eastward out of their ages-long homeland along the Zuni River. Within a couple decades they built a dozen large and small pueblos along the arc of the Zuni Mountains. Atsinna was a larger one of those pueblos.
Today, there is a paved 1/2 mile trail leading from the parking area to the pool of water at the foot of the cliff. If you have more time to explore, the 2-mile trail (includes the journey to the pool and past the inscriptions) to the top of the sandstone bluffs (250 feet of elevation gain) is well worth the hike for the views alone, never mind the chance to visit the ruins of Atsinna. While you're climbing the trail, keep in mind that for 75 years, the ancients sometimes carried water up this hill to Atsinna. They made pottery to carry and store the water. They also stored their corn and beans in pottery.
After about 75 years of occupation, the weather pattern dried up again and the Zuni Mountain pueblos were abandoned. Most of the people returned to the west, to found several pueblos in the valley of the Zuni River. The abandonment of Atsinna also coincides pretty closely with the beginning of Pottery Mound to the east.
In one of the kivas excavated at Atsinna a polychrome geometric wall mural was found. That mural was dated to have been painted between 1275 and 1300 CE, before the founding of Pottery Mound. Most kivas found with wall murals have murals that depict geometric designs. At Pottery Mound that changed.
The findings of the archaeologists support Zuni claims that Atsinna and its immediate neighbors were outlying villages of their people back in the day. There was a short-lived migration from Zuni to Acoma and then to Pottery Mound between 1395 and 1415. Then Pottery Mound was abandoned, the out-migration beginning around 1475 and by 1500, everyone had gone back to wherever their families had come from.