Binder-free electrospining approach for fabricating bimetallic chalcogen electrodes is essential for cost- and time-cutting but challenging. Herein, we propose a novel direct spray technique in electrospinning method to fabricate binder-free electrospun nickel cerium selenide nanofiber (NCSNF) structured materials. The effect of the applied electrospinning voltage on the average fiber diameter is analyzed. Electrospinning voltage of 25 kV is applied for obtaining an average fiber diameter of < 100 nm (87 nm) with rough interconnected nanofibers. The optimized NCSNF electrode exhibits remarkable long-term cycling stability over 50,000 galvanostatic charge–discharge (GCD) cycles. Furthermore, radish-derived nanolayered carbon (RDNLC) is synthesized via pyrolysis and its electrochemical properties are evaluated. The optimized NCSNF and RDNLC electrodes are employed to fabricate a polyvinyl alcohol–potassium hydroxide gel electrolyte-based quasi-solid-state asymmetric supercapacitor (ASC). The quasi-solid-state ASC delivers a high energy density value of 22 Wh kg−1 with 85% capacitance retention and 95% Coulombic efficiency over 40,000 GCD cycles, and upon being extended to the 50,000 GCD cycles, the capacitance retention and Coulombic efficiency reached 71% and 95%, respectively. A solar-charged wristband-like device is designed as a wearable supercapacitor, and the integrated device is attached to the human hand for powering electronic gadgets in contorted states, thus demonstrating its potential for wearable applications.