No, you do not need to make any payment for your sponsorship application. However, after you arrive in Canada, sponsors may expect you to contribute to your own settlement costs from the funds you bring with you.
Quebec has its own process to sponsor refugees. This means that the rules private sponsors in Quebec must follow are different from the rest of Canada. If your sponsor is from Quebec and you have questions, contact Immigration, Diversité et Inclusion. This is the part of the Quebec provincial government that deals with immigration.