Final answer:
The Technical Standards and Safety Authority (TSSA) is the organization in Ontario that has the authority to field approve appliances on-site.
Step-by-step explanation:
The organization that can field approve appliances on-site in Ontario is the Technical Standards and Safety Authority (TSSA). The TSSA is an independent authority responsible for administering and enforcing regulations concerning the safety of boilers, pressure vessels, and other types of equipment. For appliances to be legally installed and used in Ontario, they often need to be approved by the TSSA, especially if the appliances are considered to be potentially hazardous or involve gas, fuels, or pressure systems. Approval by the TSSA ensures that the equipment meets specific safety standards and regulations, which is crucial for the wellbeing of the public and for compliance with provincial law.