Given a positive integer \(n\), let \({\mathbb H}={\mathbb R}^{n-1}\times {\mathbb R}_+\) be the upper half-space where \({\mathbb R}_+\) denotes the set of all positive real numbers. For \(\alpha>-1\) and \(1\leq p<\infty\), the \(\alpha\)-weighted harmonic Bergman space \(b^p_\alpha=b^p_\alpha({\mathbb H})\) (in the authors' notation) is the Banach subspace of \(L^p({\mathbb H}, dV_\alpha)\) consisting of all harmonic functions where \(V_\alpha\) denotes the weighted measure \(dV_\alpha(z)=z_n^\alpha\, dz\) (\(z_n\) is the last coordinate of \(z\in {\mathbb H}\)). In this paper the authors first find the weighted harmonic Bergman kernels in terms of fractional derivatives of the extended Poisson kernel and then estimate those kernels to establish the \(L^p\)-boundedness (\(1