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Low-temperature specific heat Cp is measured on Ba(Fe1-xCox)2As2 single crystals in a wide doping region. A sizeable residual specific heat coefficient γo is observed in the low temperature limit of all samples. The specific heat jump near Tc, i.e. ΔCp/T/T_c, is also determined. It is found that -γo, ΔCp/T/T_c and Tc all share a similar evolution with doping. These can be well understood within the model of S± pairing symmetry when accounting for the cobalt-dopants as unitary scattering centers in the FeAs planes. Our results reveal a non-trivial impact of impurity scattering in FeAs-based.