Measurement of the branching fractions of the decays Λ_𝑐⁺ →Λ⁢𝐾⁰_𝑆⁢𝐾⁺, Λ_𝑐⁺ → Λ⁢𝐾⁰_𝑆⁢𝜋⁺, and Λ_𝑐⁺  →Λ⁢𝐾^*+

Studies are performed of the Cabibbo-favored decay Λ+𝑐→Λ⁢𝐾0𝑆⁢𝐾+ and the singly Cabibbo-suppressed decay Λ+𝑐→Λ⁢𝐾0𝑆⁢𝜋+, based on a sample of 𝑒+⁢𝑒− collision data, corresponding to an integrated luminosity of 4.5  fb−1, accumulated at center-of-mass energies between 4599.53 MeV and 4698.82 MeV with the BESIII detector. The decay Λ+𝑐 →Λ⁢𝐾0𝑆⁢𝜋+ is observed for the first time. The branching fractions of Λ+𝑐 →Λ⁢𝐾0𝑆⁢𝐾+ and Λ+𝑐 →Λ⁢𝐾0𝑆⁢𝜋+ are measured to be (3.04 ±0.30 ±0.16) ×10−3 and (1.73 ±0.27 ±0.10) ×10−3, respectively, where the first uncertainties are statistical and the second are systematic. These results correspond to the most precise measurement of these quantities for both decays. Evidence of a 𝐾*+ contribution in the Λ+𝑐 →Λ⁢𝐾0𝑆⁢𝜋+ decay is found with a statistical significance of 4.71⁢𝜎. The branching fraction of Λ+𝑐 →Λ⁢𝐾*+ is calculated under three possible interference scenarios, with the significance increasing to 5.03⁢𝜎 when interference is taken into account.