Summary: In this paper, we focus on the backward diffusion problem with the Caputo fractional derivative operator in time and a general spatial nonlocal operator. For \(T>0\) and \(s\in[0,T)\), we consider the problem \((\mathbb{P}_s)\) of recovering the distribution \(u(\mathbf{x},s)\) from a measure of the final data \(u(\mathbf{x},T)\) for the following non-homogeneous time-space fractional diffusion equation \[ D_t^\alpha u(\mathbf{x},t)+K_{\boldsymbol{\beta}}L_\gamma u(\mathbf{x},t)=f(\mathbf{x},t)\text{ in }\mathbb{R}^n\times(0,T) \] subject to the final condition \(u(\mathbf{x},T)=u_T(\mathbf{x})\) in \(\mathbb{R}^n\). The derivative orders and the nonlocal operator are perturbed with noises. Firstly, for \(0<s<T\), we prove the well-posedness of Problem \((\mathbb{P}_s)\) by studying the unique existence and continuity with respect to the derivative orders, the source term as well as the final value of the solution. Secondly, for \(s=0\), we verify the ill-posedness of Problem \((\mathbb{P}_0)\) and use the method of modified iterated Lavrentiev to construct a regularization solution from inexact data and inexact derivative orders. We apply a modified form of the discrepancy principle to choose regularization parameter and establish new optimal convergence estimates between the exact solution and its regularized approximation.