The Lagrangian of the Yang-Mills fields is given by \begin{align} \mathcal{L}=-\frac{1}{4} F^a_{\mu\nu}~ F_a^{\mu\nu} +\bar{\psi}(i\gamma^{\mu} D_{\mu})\psi- m~ \psi \bar{\psi} \end{align}
where:
\begin{align} D_\mu \psi = \partial_\mu \psi - i g~ t^a_{ij}~ A_\mu^a~ \psi\\ F_{\mu\nu}^a = \partial_\mu A^a_\nu - \partial_\nu A_\mu^a + i g f^{abc} A^b_\mu A_\nu^c \end{align}
I try to get the Noether current here: so starting by the equations of motions:
$ \frac{\partial \mathcal{L}}{\partial\psi} - \partial_\mu \frac{\partial \mathcal{L}}{\partial(\partial_\mu\psi)} = 0 ~~~~~~~~~~(1)\\ \frac{\partial \mathcal{L}}{\partial\bar{\psi}} - \partial_\mu \frac{\partial \mathcal{L}}{\partial(\partial_\mu\bar{\psi})} = 0~~~~~~~~~(2) \\ \frac{\partial \mathcal{L}}{\partial A_\mu} - \partial_\nu \frac{\partial \mathcal{L}}{\partial(\partial_\nu A_\mu)} = 0 ~~~~~~~(3)\\ $
These yield:
$ g \bar{\psi} \gamma^\mu A_\mu^a - m \bar{\psi} -i \partial_\mu \bar{\psi} \gamma^\mu = 0~~~~~~~~(4)\\ g \gamma^\mu A_\mu^a \psi - m \psi = 0~~~~~~~~~~~(5)\\ g\bar{\psi} \gamma^\mu t^a_{ij} \psi_j + g f^{abc} A^b_\nu F^{c~\mu\nu}= \partial_\nu F^{a~ \nu \mu}~~~~~~~~(6) $
Clearly (6) is the right equation of motion of the Yang Mills theory with a conserved current : $J^{a~ \mu} = g\bar{\psi} \gamma^\mu t^a_{ij} \psi_j$ , see for instance Peskin's book Equation(15.51) . Now I have extra terms in (4) and (5) what's wrong I made?