The electronic structure of the condensed matter is a key rule to determine the physical characteristics such as electrical, magnetic, and thermal properties. From 1808, research on electrides is ignited since the discovery of the solvated electron in ammonia liquids. Electrides are ionic crystals which have interstitial electrons acting as anions in structural cavities. Engineering of electronic structure in electrides is classified by dimensional modification and localization of interstitial electrons for exotic electrical and magnetic characteristics, respectively. Furthermore, since the discovery of the first heavy fermion compound CeAl3 and the first superconducting heavy fermion compound CuCe2Si2 in 1975 and 1979, respectively, the research on hybridization of f-electrons that originated in rare earth or actinide elements are focused on to understand the condensed matter physics in extremely low temperature. In this thesis, I mainly research on rare-earth metal-rich carbide materials to modulation of electronic dimension, localization, and correlation for unconventional characteristics. In the first part of the thesis, I demonstrate two-dimensional layer structured Y2C electride that the world first, centimeter scale of electrides with exotic magnetic characteristics due to the localized anionic electrons along the 2D layers. To demonstrate the magnetic characteristics of Y2C electride due to the interstitial anionic electrons (IAEs) along the 2D layers, I performed not only electrical and magnetic measurements along each direction of perpendicular and parallel to the c-axis but also theoretical spin-polarized DFT calculations to support experimental results. In the second part of the thesis, I modified enhancement of magnetic ordering of IAEs in Y2-xScxC electrides through the Sc substitution to Y site to compress structural cavities where IAEs located in. The modulating electronic structure that improved the spin alignment of IAEs lead to the strong magnetic ordering of electrides via negative chemical pressure. In the third part of the thesis, I realized a strong correlation of electrons using electronic structure engineering for hybridization of f-electrons in the Gd3SnC heavy fermion ferromagnet. Strong correlations between f-electrons in Gd3SnC revealed up to 700 times higher specific heat capacity compared to conventional Cu or Al metals. To clarify the origin of strong hybridization between f-electrons, I adopt measurements such as resistivity, magnetic moments, and heat capacity down to extremely low temperature. To prove the role of electronic structure in Gd3SnC heavy fermion compound, I performed La substitution to Gd site to reduce the hybridization between f-electron via eliminating the number of f-electrons. In conclusion, I demonstrated the modulation of the electronic structure affecting unconventional physical characteristics such as magnetic ordering in Y2C electrides and coexistence of heavy fermion and ferromagnetic states in Gd3SnC compounds. As a result, I expect that the research of electronic structure leads to new insight for electronic and magnetic research in condensed matter physics.