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In this work, we systematically study the mass spectra and strong decays of 1P and 2S charmed and charmed-strange baryons in the framework of non-relativistic constituent quark models. With the light quark cluster–heavy quark picture, the masses are simply calculated by a potential model. The strong decays are studied by the Eichten–Hill–Quigg decay formula. Masses and decay properties of the well-established 1S and 1P states can be reproduced by our method. $$\Sigma _c(2800)^{0,+,++}$$ can be assigned as a $$\Sigma _{c2}(3/2^-)$$ or $$\Sigma _{c2}(5/2^-)$$ state. We prefer to interpret the signal $$\Sigma _c(2850)^0$$ as a $$2S(1/2^+)$$ state although at present we cannot thoroughly exclude the possibility that this is the same state as $$\Sigma _c(2800)^0$$ . $$\Lambda _c(2765)^+$$ or $$\Sigma _c(2765)^+$$ could be explained as the $$\Lambda _c^+(2S)$$ state or $$\Sigma ^+_{c1}(1/2^-)$$ state, respectively. We propose to measure the branching ratio of $$\mathcal {B}(\Sigma _c(2455)\pi )/\mathcal {B}(\Sigma _c(2520)\pi )$$ in the future, which may disentangle the puzzle of this state. Our results support $$\Xi _c(2980)^{0,+}$$ as the first radial excited state of $$\Xi _c(2470)^{0,+}$$ with $$J^P=1/2^+$$ . The assignment of $$\Xi _c(2930)^0$$ is analogous to $$\Sigma _c(2800)^{0,+,++}$$ , i.e., a $$\Xi ^\prime _{c2}(3/2^-)$$ or $$\Xi ^\prime _{c2}(5/2^-)$$ state. In addition, we predict some typical ratios among partial decay widths, which are valuable for experimental search for these missing charmed and charmed-strange baryons.