Using off-brand inks WILL NOT void your printer warranty. The company will tell you this, but according to federal law they cannot void your warranty for it.
Now what I can tell you is that not all inks are the same, and using off-brand inks may not be the same quality as the printer company's inks. I've used replacement inks in my Brother, Epson, Canon, Lexmark, Samsung, and Konica printers, and the only ones that were "allergic" to the off-brand inks were the laser printers. (Don't judge me, I have a printer fetish.)
If you do happen to purchase an off-brand ink, I would suggest purchasing from a vendor with a money back guarantee.