The layered bismuth oxy-sulfide materials, which are structurally related to the Fe-pnictides/chalcogenides and cuprates superconductors, have brought substantial attention for understanding the physics of reduced dimensional superconductors. We have examined the pairing symmetry of recently discovered BiCh$_2$-based superconductor, La$_mathrm{1-x}$Ce$_mathrm{x}$OBiSSe with $x$ = 0.3, through transverse field (TF) muon spin rotation measurement, in addition we present the results of magnetization, resistivity and zero field (ZF) muon spin relaxation measurements. Bulk superconductivity has been observed below 2.7 K for $x$ = 0.3, verified by resistivity and magnetization data. The temperature dependence of the magnetic penetration depth has been determined from TF-$mu$SR data can be described by an isotropic two-gap $s+s$ wave model compared to a single gap $s$- or anisotropic $s$-wave models, the resemblance with Fe-pnictides/chalcogenides and MgB$_2$. Furthermore, from the TF-$mu$SR data, we have determined the Londons penetration depth $lambda_mathrm{L}(0)$ = 452(3) nm, superconducting carriers density $n_mathrm{s}$ = 2.18(1) $times$10$^{26}$ carriers/m$^{3}$ and effective mass enhancement $m^{*}$ = 1.66(1) $m_mathrm{e}$, respectively. No signature of spontaneous internal field is found down to 100 mK in ZF-$mu$SR measurement suggest that time-reversal symmetry is preserved in this system.
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