There may exist seven Dbar(*)Σc
(*) hadronic molecular states. We construct their corresponding interpolating currents, and calculate their masses and decay constants using QCD sum rules. Based on these results, we calculate their relative production rates in Λb
0 decays through the current algebra, i.e., B(Λb
0 → Pc K-):B(Λb
0 → Pc' K-) with Pc and Pc' two different states. We also study their decay properties through the Fierz rearrangement, and further calculate these ratios in the J/ψp mass spectrum, i.e. B(Λb
0 → Pc K- → J/ψ p K-):B(Λb
0 → Pc' K- → J/ψ p K-). Our results suggest that the Dbar*Σc
* molecular states of J(P) = 1/2(-) and 3/2(-) are possible to be observed in future experiments. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.