Ah, gotcha.
Okay, the first step is this: Make sure that your sabre cat counts as a summonable creature. Open it up and check the "Summonable" option.
Then, what you want to do is look at the magic effects for the other summon spells. Pick one that's close in cost/casting level to what you want, right click on it and duplicate. Open up the new, duplicate record, change the first Assoc. Item to point to your sabre cat (which is only on the list because of the first step), and give the effect a new, unique ID. When it asks you whether you want to create a new record, say no (you already did that with the duplication) and then yes when it asks if you're sure.
Then move up the chain. Magic effects are used in Spells, so find the spell for the magic effect you copied earlier, and duplicate it. Then change the effect of that spell to the effect you just made, rename the spell, and give it a new ID.
Next you have to make a book that will teach you the spell. Again, copy the spell tome for the spell you copied, and change the spell it teaches to the one you just made. (Don't forget to give it a new id and a new name! I know I keep mentioning this, but I find it annoying to have forgotten this and have to go back and fix it.)
Finally, you have to put the spell tome somewhere in the world your player can get to it. There are a few options. In order of ease, you can put it in spell vendors, place it in the world somewhere for you to pick up, or make a quest that will add it to your inventory automatically. (You can skip this step entirely, and indeed the spell tome step, if you're okay with just using the console to teach yourself the spell.)
For spell vendors: Find a leveled list called ConjurationSpellTomes00All, or 25All, etc., depending on whether you want this to be sold as a novice, apprentice, etc. spell. Open it up and drag your spell tome in. Save, and you're done. Spell vendors will now sell it (though you may have to wait for their inventories to reset before it'll appear, which can also be accomplished by saving, beating the crap out of them, then reloading the save).
To place it in the world, pick your location and use the Cell View window to open up that location in the Render Window. Drag the spell tome into the render pane, then move the book into position. You'll need to use some
keyboard shortcuts to do this effectively, notably E (which will allow you to move it with the little handles that pop up), W (rotate), T (center on top of the object), and F (make it "fall" down to the nearest surface). Once you have it where you want it, you may also want to hit the Havok Settle button along the top bar, which will simulate the physics of everything settling into more natural positions.
To put it in a quest... that's a little more complicated than I think either you or I want to get into right now
.
Note that this last step, making it available to you to find in the world, is the part where mod conflicts might enter. If you have other mods which use the same methods to introduce changes to the game world, they might overlap, in which case only one of them will actually appear.
And just so you know, it's often easiest to learn how to make something in the Creation Kit by looking at similar things that are already in the game data (which is why I said to duplicate from existing records throughout this explanation). If you see an option or check box or field or whatever that you're not sure what it does, the wiki is the first place to look, but other sources might be able to explain as well. There's no guarantee that anyone will even know what you're trying to learn, though. The CK is incredibly poorly documented.