"To quote a fee" means to provide a specific amount of money that will be charged for a particular service or job. It is basically mentioning the price or cost for something. Full definition
Maybe they just quote fees for ten minutes, but you spend two hours detailing the various options and the strengths and weaknesses of each route. (lawyerist.com)
Please note that we can not quote fees over the phone. (slco.org)
The attorney you're considering hiring should be able to quote you a fee based on your unique circumstances. (betterbankruptcy.com)