## 1 Introduction  
An emerging device for storing and converting energy, the supercapacitor has been used in place of batteries and conventional capacitors. They possess many advantages and potential due to various reasons. They exhibit high power density and great efficiencies along with a high capability of charge/discharge and long cyclic stability [1]. There are many applications of supercapacitors in different fields that include auto-motives and portable electronic devices as well as aerospace and military fields and many more. Mainly, supercapacitors are categorized into two types. First, is electric double-layer capacitors (EDLCs) and the second is pseudocapacitors (PCs). The EDLCs have higher values of capacitance in contrast with conventional capacitors due to the short distance up to the nanometer level between the double layers [2]. The ability of charge storage in EDLCs on the surface of electrode materials depends upon the adsorption and desorption of electrolyte ions. Despite the high reversibility and perfect cyclic performance of EDLCs, their energy density is still low which limits their applications. The other form of supercapacitors, PCs, can store charge on the surface of the electrode material having fast faradaic redox reactions and rely on high reversibility confirming the battery-like nature [3, 4]. The electrolyte ions that cause fast faradaic reactions can be inserted and deserted on the interfaces between electrolyte and electrode. The specific capacitance of PCs is greater than EDLCs. Commonly used electrode materials in PCs are oxides, sulfides, hydroxides, and phosphides of transition metals. We synthesized this nanocomposite using oxides of nickel and cerium. The properties of EDLCs and PCs can be combined in hybrid supercapacitors (HSCs) in which negative electrode materials are made up of carbon materials while positive electrode materials are composed of battery-like transition metal oxides (TMOs) [5; 6]. This approach also enhances the potential window or the working voltage range of the device. This increase in the potential window is directly linked with the energy density of the electrode material which is measured using: E = \(\frac{1}{2}\) CV\({}^{2}\). In the recent decade, a lot of work has been devoted to the positive electrode materials that have high energy density, specific capacitances, and are eco-friendly [7; 8; 9]. Rare earth metal oxide, cerium oxide, is an intensively studied material because of its vast applications such as in portable devices, electrical vehicles, and sustainable energy devices. The composite of cerium oxide can be used for catalytic redox reactions and to clean the exhaust of automobiles. The reversible chemical reaction depends upon the chemical potential of oxygen between the two cerium oxides that can cause a catalytic effect. These two cerium oxides are oxygen-poor Ce\({}_{2}\)O\({}_{3}\) and oxygen-rich CeO\({}_{2}\). To expand the catalytic process of cerium oxide it is much needed to find novel metal ions that can be doped in CeO\({}_{2}\) which can further improve the oxygen storage capacity [10; 11]. In this regard, researchers working across the globe have attempted to mix the oxides of rare-earth metals, transition metals, and alkaline metals with Ce sub-lattice. To compensate charges in the lattice, the anion vacancy sites can be created by changing Ce\({}^{4+}\) with Ce\({}^{2+}\) and Ce\({}^{3+}\) cations which leads to enhance the ionic conductivity for oxygen. However, the doping is carried out under dopant selection criteria i.e., the ionic radius of dopant must be comparable to the ionic radius of the host [12]. From the literature, it is noticed that the addition of transition metal ions is suitable for doping in CeO\({}_{2}\). Generally, the composites of CeO\({}_{2}\) with Cu doping represent enhanced catalytic performances as well as high oxygen storage capacities and high specific surface areas [13].