You're asking several different things and this is a pet love of mine, so this is going to be a long post as I address each of them.

The population didn't go extinct, but the culture of that particular group of Alans did (note that this is not all Alans; I'll get to that later). The Huns invaded the Alans' old stomping grounds in 370, and the Alan tribes that didn't join them were pushed westward. One group joined up with the Vandals and Suevi as they pushed further West, invading Gaul, then continuing on to the Iberian Peninsula. They left behind many place names across both regions derived from their name (e.g., Allainville in Gaul and Alenquer in Iberia), as well as in the name of a type of Iberian dog descended from their own mastiffs, the Alaunt. The various molosser-type dogs of Western Europe are likely in part descended from the dogs introduced by the Alans.

Their king, Attaces, was killed in an early 5th century battle with the Visigoths, at which point the group asked Gunderic, the king of the Vandals to take his place. Holders of that duel crown later called themselves "rex Wandalorum et Alanorum", King of the Vandals and Alans. This is when they start losing their separate cultural identity.

When the Vandals decided to pick up and go on the move again in 429, the Alans had to go too since they were now under the same leader. It's probable some stayed behind, but most went with the Vandals, who ended up establishing a kingdom along the northern Maghreb coast, including much of modern Tunisia and part of Algeria.

Now that that group isn't Alan anymore, I'm going to step back and address your mention of the Ossetians. The Ossetians are not descended from the Alans who traveled westward. They're descended from a different group of Alans who stayed in the steppes until being pushed southward up against the Caucasus by the later Mongol invasion. This group remained there and began interacting much more heavily with the various Caucasian ethnicities (actual Caucasian, not as in "generic white people"). Once the Huns were no longer a strong force in the region, they expanded back into some of their old territory and founded the medieval kingdom of Alania. Alania had such close ties to their Georgian neighbors that there was intermarriage in the royal family. But the two cultures do remain separate and this group of Alans are the ones who eventually became the Ossetians.

In the meantime, though, the Mongols conscripted part of the Alans who had remained behind after the Hunnic invasion into their army. This group (along with other conscripted soldiers) was actually taken back to China, where they participated in the usurpation of the Song Dynasty and establishment of the Yuan Dynasty. There are, of course, no Alan-identifying groups in China or Mongolia now. They assimilated with the Mongols, in the Asud tribe.

There's also the related Jasz of Hungary, who aren't descended from the Alans, but from other Sarmatian peoples. The name's similar to the Iazyges, but the Roxolani were also in the right place at the right time. To my understanding it's not clear how much each group contributed to the Jasz. The Jasz actually managed to keep their language alive until the 15th century.

And I'm afraid I have to run now since that took so long to write... I'll come back and add my citations later today.

EDIT: Citations, now that I'm back home

For general early Alan info, there's the Osprey Publishing book, The Sarmatians 600BC-450 AD.

From there, hop over to The New Penguin Atlas of Medieval History by Colin McEvedy. It's provides a big picture view of how various migrations and invasions interacted with one another during the Middle Ages. It covers all the way from raiding with the Vandals through Alania, but doesn't discuss them after the fall of the kingdom since Ossetians have never been big players at that scale (you'd want to look at sources focusing on the Caucasus region for that).

For discussions of the Alans in China, you'll want to actually search for info on Mongol history. The Alans/Asud are just on the sideline in the much bigger story of the Mongolian Empire, so you only ever get snippets about them. One example of a book is The Empire of the Steppes: A History of Central Asia, by Rene Grousset