This study investigates the dielectric properties of various mixtures of potential gaseous cryogens containing helium (He), hydrogen (H2), neon (Ne), and nitrogen (N2) under extended temperature and pressure ranges for high-temperature superconducting applications. We present the results of the Boltzmann analysis on a variety of binary and ternary gas mixtures in terms of the electron energy distribution function and the coefficients that represent the electron kinetic process, including the density-reduced ionization coefficient (α/N), the density-reduced attachment coefficient (η/N), the density-reduced effective ionization coefficient ((α−η)/N), and the density-reduced critical electric field ((E/N)cr). The study provides insights into the important characteristics and correlations that lead to the enhanced dielectric strength of gas mixtures and predicts further enhancements in the dielectric strengths of He-H2 mixtures by introducing the ternary mixtures of He-H2-N2. The study results recommend the potential ternary gas mixtures suitable for various cryogenic operating conditions and aid in the development of superconducting applications incorporating gaseous cryogens.