Squelch is a verb meaning (1) to crush by or as if by trampling, (2) to silence, and (3) to suppress. Quelch appears in unabridged dictionaries, but it has never been a well-established or widely used word. It is just a fusion of squelch and the similar verbs quell and quash, both of which mean to put down or suppress forcibly (among their other definitions). Quench might be in the mix as well.
Quelch may someday enter the language more broadly, but it doesn’t seem to be gaining ground, and it remains rare after 500 years of intermittent use. So unless you wish to be a pioneer, try squelch, quell, quash, or another fitting word instead.
In these examples, quelch could be replaced with squelch:
Order the ‘Schmitter’, a cheesesteak with fried salami, tomato, and secret sauce will be sure to quelch even the hungriest belly. [Yahoo! Sports]
It’s too soon to know whether it will quelch the debate over the existance of climate change but an inquiry has cleared climate researchers of malpractice. [CBS News]
He made a crucial baseline jumper and steal in the final seconds to quelch a Nets rally. [Daily Times]
[A]nd the firm has tried to quelch political outcrys in the U.S. against the deal. [Travel Agent]