We investigate the Hyers–Ulam–Rassias stability of a generalized quadratic functional equation of the asymmetric four-function form $F(x+y)+G(x-y)=L\left(x\right)+M\left(y\right)$, where F, G, L, and M are unknown mappings. This study is conducted within the framework of non-Archimedean normed spaces over the p-adic numbers. Our approach employs a separation technique, analyzing the even and odd parts of the functions to establish stability results. We show that all four functions are approximated by a combination of a quadratic function and two additive functions.