The effects of electron (Ir) and hole (Re) doping on the hybridization gap and antiferromagnetic order have been studied by magnetization, muon spin relaxation ($mu^+$SR), and inelastic neutron scattering on the polycrystalline samples of Ce(Os$_{1-x}$Ir$_x$)$_2$Al$_{10}$ ($x$ = 0.08 and 0.15) and CeOs$_{1.94}$Re$_{0.06}$Al$_{10}$. $mu^+$SR spectra clearly reveals magnetic ordering below 20 and 10 K for $x$ = 0.08 and 0.15 samples respectively with a very weak signature of oscillations of the muon initial asymmetry at very short time scale. Our important findings are that small amount of electron doping (i) completely suppress the inelastic magnetic excitations near 11 meV down to 2K, which were observed in the undoped compound, and the response transforms into a broad quasielastic response and (ii) the internal field at the corresponding muon site is remarkably enhanced by about ten times compared with the parent compound. On the other hand with small amount of hole (3% Re) doping the intensity of the inelastic magnetic excitations near 11 meV is reduced significantly. The main origin of the observed doping effect is an extra 5$d$ electrons being carried by Ir and a hole carried by Re compared with that the Os atom. The obtained results demonstrate a great sensitivity of the carrier doping and provides additional ways to study their anomalous magnetic properties.
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