Im having trouble finding quicksilver ore to upgrade my Nordic sword. Does anyone know where to get some?

blacksmiths have them.. depending on ur level i have no problem finding them im level 39. Just go to a lot of blacksmiths in skyrim if u have to. there is a quicksliver mine i believe??? i just cant remember where

There is a quicksilver mine in Dawnstar. And as previously said, hit up blacksmiths. Most should sell at least a few ingots and ore.

If you're looking for it in Solstheim, the Altar of Thrond cave has a couple veins.

There are also two veins near Shimmermist cave. The veins respawn after 30 in-game days (give or take).

If you can't be bothered to Mine Veins, and want a more "Combat Involving" way of doing things, kill loads of Ash Spawn. They seem to drop every kind of ore, even multiple ores at the same time.

But I'de suggest going to Quicksilver Mine in Dawnstar. It's the more easier choice.

I have found every kind of ore on the Ash Spawn.

I got a rock.

As other posters have mentioned, Dawnstar is by far the easiest place to get ore and smelt it immediately. Blacksmiths will occasionally carry it, of course, and don't restrict yourself to just the towns, either. Hit up those quartermasters in the army camps, either Imperial, Stormcloak, or both if you haven't picked a side yet. They tend to be fairly near each other, so you can hit them on the way to a major town (with the exception of Morthal and Winterhold; these towns don't need nails to hold things together, they have ice!).

If you have Dawnguard installed there's lots of quicksilver ore

As was said, there's a mine in Dawnstar with about 5 Quicksilver veins. Other than that i've found a few veins on the northern coastline between Dawnstar and Solitude.

there are at least 2 next to the tower stone