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The use of the Silicon-on-Insulator (SOI) platform has been prominent for realizing CMOS-compatible, high-performance photonic integrated circuits (PICs). But in recent years, the silicon-nitride-on-silicon-dioxide (SiN-on-SiO$_2$) platform has garnered increasing interest as an alternative to the SOI platform for realizing high-performance PICs. This is because of its several beneficial properties over the SOI platform, such as low optical losses, high thermo-optic stability, broader wavelength transparency range, and high tolerance to fabrication-process variations. However, SiN-on-SiO$_2$ based active devices such as modulators are scarce and lack in desired performance, due to the absence of free-carrier based activity in the SiN material and the complexity of integrating other active materials with SiN-on-SiO$_2$ platform. This shortcoming hinders the SiN-on-SiO$_2$ platform for realizing active PICs. To address this shortcoming, we demonstrate a SiN-on-SiO$_2$ microring resonator (MRR) based active modulator in this article. Our designed MRR modulator employs an Indium-Tin-Oxide (ITO)-SiN-ITO thin-film stack, in which the ITO thin films act as the upper and lower claddings of the SiN MRR. The ITO-SiN-ITO thin-film stack leverages the free-carrier assisted, high-amplitude refractive index change in the ITO films to effect a large electro-refractive optical modulation in the device. Based on the electrostatic, transient, and finite difference time domain (FDTD) simulations, conducted using photonics foundry-validated tools, we show that our modulator achieves 280 pm/V resonance modulation efficiency, 67.8 GHz 3-dB modulation bandwidth, $\sim$19 nm free-spectral range (FSR), $\sim$0.23 dB insertion loss, and 10.31 dB extinction ratio for optical on-off-keying (OOK) modulation at 30 Gb/s.