Teriyaki sauce, like most sauce, has a very low smoke point. It can be used in addition to oil of you want to caramelize things, but as a heat transfer medium it is more useless than water. Use oil and add the sauce at the end during cool down.

Avocado oil has one of the highest smoke points and I pretty much only use it unless I’m doing potato stuff, which I’ll use canola for.

Both of the proposed have ingredients that cook and char to solids if you cook them at temperatures you want to fry at. You need something that can take the heat and transfer it. You need a fat or an oil. Maybe a heavy sugary water like applesauce could be used but it’s not boiling than frying.

Teriyaki sauce has sugar, so it’s going to burn right away.

Just use the appropriate oil.

Oil is what you use to keep things from sticking.

Side note: you might be better off using said sauces at the end of your fry when your dish is basically done, not to replace oil but just for flavor (and to cook some of the vinegar out of said sauce). I do that with some Japanese barbecue sauce when frying vegetables, but it’s also a thin/vinegary sauce (I wouldn’t try it with something made for dipping).

You can’t fry with any water-based liquid, as those can only heat to the boiling point of water, and once that’s gone they’ll burn

Teriyaki can not be.

I don’t know what magi is.

Are you all out of oil?

Both are not oil, they are condiments. It will simply burn and char before any reasonable oils smoke point.