We report a study of Λc+→Λh+ and Λc+→Σ0h+ (h=K,π) decays based on a data sample of 980fb-1 collected with the Belle detector at the KEKB energy-asymmetric e+e- collider. The first results of direct CP asymmetry in two-body singly Cabibbo-suppressed (SCS) decays of charmed baryons are measured, ACPdir(Λc+→ΛK+)=+0.021±0.026±0.001 and ACPdir(Λc+→Σ0K+)=+0.025±0.054±0.004. We also make the most precise measurement of the decay asymmetry parameters (α) for the four modes of interest and search for CP violation via the α-induced CP asymmetry (ACPα). We measure ACPα(Λc+→ΛK+)=-0.023±0.086±0.071 and ACPα(Λc+→Σ0K+)=+0.08±0.35±0.14, which are the first ACPα results for SCS decays of charmed baryons. We search for Λ-hyperon CP violation in Λc+→(Λ,Σ0)π+ and find ACPα(Λ→pπ-)=+0.013±0.007±0.011. This is the first time that hyperon CP violation has been measured via Cabibbo-favored charm decays. No evidence of baryon CP violation is found. We also obtain the most precise branching fractions for two SCS Λc+ decays, B(Λc+→ΛK+)=(6.57±0.17±0.11±0.35)×10-4 and B(Λc+→Σ0K+)=(3.58±0.19±0.06±0.19)×10-4. The first uncertainties are statistical and the second systematic, while the third uncertainties come from the uncertainties on the world average branching fractions of Λc+→(Λ,Σ0)π+. © 2023 Science China Press