  We report a doping, magnetic field and low-temperature dependent study of the
specific heat of the iron-arsenide Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ at
under (x=0.045), optimal (x=0.08) and overdoped (x=0.103 and 0.105) regimes. By
subtracting the lattice specific heat the temperature and magnetic field
dependence of the electronic specific heat has been studied. The temperature
and field dependencies of the superconducting part of $C_{p}$ exhibit similar
behavior for all doping concentrations. The temperature variation of the
electronic specific heat as well as its field dependence cannot be described by
a single isotropic s-wave gap, pointing to a complex gap structure in the
system. The lack of doping dependence indicates that the gap structure does not
change significantly as a function of doping. We also observe a significant
residual linear term of unknown origin in the specific heat of
Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ which suggests that inhomogeneity may be
an important factor in Co-doped BaFe$_{2}$As$_{2}$
