The best analogue of your nation is actually Tibet. The Tibetan plateau sits some 4.5kms above sea level, and they have crops up there which look reasonably similar to those in lower altitudes, but with some differences.
The most common crop in Tibet is something called qingke, which is a form of barley that grows particularly well in high altitudes and is both cold and drought resistant. But, they also grow wheat, rice, potatoes and the like. If you look at their farming practices in the same link, even on the side of mountains they tend to terrace their land, putting specific crops on different terraces for the season. I'm assuming that they would rotate crops between terraces for the health of the soil but I couldn't find that information in the link.
Based on my readings, barley is a common crop for high altitude and mountainous terrains, largely because of its hardiness. BUT, it's important to note that (IIRC) it has less than a third of the energy value of wheat, meaning you need to grow more of it to get the same value in terms of energy. I don't know offhand about the nutritional values but it would appear that barley related foods are a primary staple for Tibetan farmers so it certainly has to have at least some nutritional value in that regard other than energy.