This paper introduces a modified consensus-based real-time optimization framework for utility-connected and islanded microgrids scheduling in normal conditions and under cyberattacks. The exchange of power with the utility is modeled, and the operation of the microgrid energy resources is optimized to minimize the total energy cost. This framework tracks both generation and load variations to decide optimal power generations and the exchange of power with the utility. A linear cost function is defined for the utility where the rates are updated at every time interval. In addition, a realistic approach is taken to limit the power generation from renewable energy sources, including photovoltaics (PVs), wind turbines (WTs), and dispatchable distributed generators (DDGs). The maximum output power of DDGs is limited to their ramp rates. Besides this, a specific cloud-fog architecture is suggested to make the real-time operation and monitoring of the proposed method feasible for utility-connected and islanded microgrids. The cloud-fog-based framework is flexible in applying demand response (DR) programs for more efficiency of the power operation. The algorithm’s performance is examined on the 14 bus IEEE network and is compared with optimal results. Three operating scenarios are considered to model the load as light and heavy, and after denial of service (DoS) attack to indicate the algorithm’s feasibility, robustness, and proficiency. In addition, the uncertainty of the system is analyzed using the unscented transformation (UT) method. The simulation results demonstrate a robust, rapid converging rate and the capability to track the load variations due to the probable responsive loads (considering DR programs) or natural alters of load demand.