In this study, we discuss the existence of positive solutions for the system of $m$-singular sum fractional $q$-differential equations \begin{equation*} \begin{split} D_q^{\alpha_{i}} x_{i} & + g_i\big(t, x_1, \ldots, x_{m}, D_q^{\gamma_{1}} x_{1}, \ldots , D_q^{\gamma_{m}} x_{m} \big) \\ & +h_{i} \big(t, x_{1}, \ldots , x_{m}, D_q^{\gamma_{1}} x_{1}, \ldots, D_q^{\gamma_{m}} x_{m} \big)=0 \end{split} \end{equation*} with boundary conditions $x_{i}(0) = x_{i}' (1) = 0$ and $x_{i}^{(k)}(t) = 0$ whenever $t=0$, here $2\leq k \leq n-1$, where $n= [\alpha_{i}]+ 1$, $\alpha_{i} \geq 2$, $\gamma_{i} \in (0,1)$, $D_q^\alpha$ is the Caputo fractional $q$-derivative of order $\alpha$, here $q \in (0,1)$, function $g_{i}$ is a Carath\'{e}odory, $h_{i}$ satisfy Lipschitz condition and $g_{i} (t , x_{1}, \ldots, x_{2m})$ is singular at $t=0$, for $1 \leq i \leq m$. By means of Krasnoselskii's fixed point theorem, Arzel\`{a}-Ascoli theorem, Lebesgue dominated theorem and some norms, the existence of positive solutions is obtained. Also, we give an example to illustrate the primary effects.
