Throughout the more recent games (Morrowind, Oblivion, and Skyrim) the properties of alchemy ingredients changes dramatically. Take the Daedra Heart for example:

Morrowind properties: Restore Magicka, Fortify Endurance, Drain Agility, Night Eye

Oblivion properties: Restore Health, Shock Shield, Damage Magicka, Silence

Skyrim properties: Restore Health, Damage Stamina Regen, Damage Magicka, Fear

How is one to know which properties are canon to the lore? Are all of the properties canon, in which case some substances have more than 4 properties? (Like the Daedra Heart with 10 different properties over 3 games?)

I need to know this because I'm making an Elder Scrolls Tabletop RPG and need to figure out how alchemy will work.

Whichever you think fits best. Choose one of the games. Or mix and match. Or use all the effects. Heck, you could even come up with your own!

Also: Good luck on your tabletop! What sort of system are you using, if I may ask?

A system similar to the CODA system. 2d6 core mechanic, used for the Lord of the Rings Roleplaying Game. It's turning out great so far. Got the attributes, races, classes, birthsigns, traits (edges and flaws), class abilities, and equipment mostly done.

Just need to work on Alchemy, Magic and Spells, Bestiary, and Geography.

Alchemy is a bit finicky, and in terms of lore...well, most would typically cite that gameplay doesn't necciscairly equal lore as far as consistency goes, since certain game mechanics are prone to change.

The way I see it, you could probably go with whatever you feel is right for the most part, or even make your own effects for them. As far as I'm aware, alchemy in the series is a pretty broad concept.