In this paper, we study the ill-posed fractional backward heat equation $$\left\{\begin{array}{ll} \frac{\partial^{\gamma} u}{\partial t^{\gamma}}={\varDelta} u,\quad x\in \mathbb{R}^{n},t\in(0,T),\\ u(x,T)=\varphi(x), \quad x\in\mathbb{R}^{n}, \end{array}\right. $$ where $\varphi $ is unknown exact data and only noisy data $\varphi^{\varepsilon}$ with $$\|\varphi^{\varepsilon}(\cdot)-\varphi(\cdot)\|_{L_{2}(\mathbb{R}^{n})}\leqslant\varepsilon $$ is available. The problem is regularized by the well-posed mollified problem $$\left\{\begin{array}{ll} \frac{\partial^{\gamma} v^{\nu}}{\partial t^{\gamma}}={\varDelta} v^{\nu},\quad x\in \mathbb{R}^{n},t\in(0,T),\\ v^{\nu}(x,T)=S_{\nu}(\varphi^{\varepsilon}(x)), \quad x\in \mathbb{R}^{n}, \end{array}\right. $$ where $\nu > 0$ and $S_{\nu}(\varphi^{\varepsilon}(x))$, a mollification of $\varphi^{\varepsilon}$ defined by the convolution of $\varphi^{\varepsilon}(x)$ with Dirichlet kernel. The error estimates $\|u(\cdot ,t)-v^{\nu }(\cdot ,t)\|_{H^{l}(\mathbb {R}^{n})}, 0\leq l$ are established for $\nu$ chosen a priori and a posteriori.