This one is easy to miss at the start of your Morrowind journey, due to the fact the quests take you out of there and toward the other locations pretty quickly. The exact location of the shard is in the courtyard of the house where you have to talk to Governor Salvi. This is a part of the starting Morrowind quest. While inside the Governor’s office, leave toward the Census and Excise Courtyard.
If you are like me and you like to explore, you’ll spot the shard from the distance by its bright glow. I’ve spotted it from a nearby river. It is just next to the courtyard’s wooden fence. If you decide to try and grab it from outside of the property, you won’t be able to. Trust me, I’ve tried it more than once.
Guarded by the wooden fence.