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. $$\Sigma _c(2800)^{0,+,++}$$ Σ c ( 2800 ) 0 , + , + + can be assigned as a $$\Sigma _{c2}(3/2^-)$$ Σ c 2 ( 3 / 2 - ) or $$\Sigma _{c2}(5/2^-)$$ Σ c 2 ( 5 / 2 - ) state. We prefer to interpret the signal $$\Sigma _c(2850)^0$$ Σ c ( 2850 ) 0 as a $$2S(1/2^+)$$ 2 S ( 1 / 2 + ) state although at present we cannot thoroughly exclude the possibility that this is the same state as $$\Sigma _c(2800)^0$$ Σ c ( 2800 ) 0 . $$\Lambda _c(2765)^+$$ Λ c ( 2765 ) + or $$\Sigma _c(2765)^+$$ Σ c ( 2765 ) + could be explained as the $$\Lambda _c^+(2S)$$ Λ c + ( 2 S ) state or $$\Sigma ^+_{c1}(1/2^-)$$ Σ c 1 + ( 1 / 2 - ) state, respectively. We propose to measure the branching ratio of $$\mathcal {B}(\Sigma _c(2455)\pi )/\mathcal {B}(\Sigma _c(2520)\pi )$$ B ( Σ c ( 2455 ) π ) / B ( Σ c ( 2520 ) π ) in the future, which may disentangle the puzzle of this state. Our results support $$\Xi _c(2980)^{0,+}$$ Ξ c ( 2980 ) 0 , + as the first radial excited state of $$\Xi _c(2470)^{0,+}$$ Ξ c ( 2470 ) 0 , + with $$J^P=1/2^+$$ J P = 1 / 2 + . The assignment of $$\Xi _c(2930)^0$$ Ξ c ( 2930 ) 0 is analogous to $$\Sigma _c(2800)^{0,+,++}$$ Σ c ( 2800 ) 0 , + , + + , i.e., a $$\Xi ^\prime _{c2}(3/2^-)$$ Ξ c 2 ′ ( 3 / 2 - ) or $$\Xi ^\prime _{c2}(5/2^-)$$ Ξ c 2 ′ ( 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.