Measurement of the absolute branching fraction of the three-body decay ${\Lambda }_{c}^{+}\to {\Xi }^{0}{K}^{+}{\pi }^{0}$ and search for ${\Lambda }_{c}^{+}\to n{K}^{+}{\pi }^{0}$, ${\Sigma }^{0}{K}^{+}{\pi }^{0}$, and $\Lambda {K}^{+}{\pi }^{0}$

The Cabbibo-favored decay ${\Lambda }_{c}^{+}\to {\Xi }^{0}{K}^{+}{\pi }^{0}$ is studied for the first time using $6.1\text{}\text{}{\mathrm{fb}}^{-1}$ of ${e}^{+}{e}^{-}$ collision data at center-of-mass energies between 4.600 and 4.840 GeV, collected with the BESIII detector at the BEPCII collider. With a double-tag method, the branching fraction of the three-body decay ${\Lambda }_{c}^{+}\to {\Xi }^{0}{K}^{+}{\pi }^{0}$ is measured to be $\left(7.79±1.46±0.95\right)×{10}^{-3}$, where the first and second uncertainties are statistical and systematic, respectively. The branching fraction of the two-body decay ${\Lambda }_{c}^{+}\to \Xi \left(1530{\right)}^{0}{K}^{+}$ is $\left(5.99±1.04±0.32\right)×{10}^{-3}$, which is consistent with the previous result of $\left(5.02±0.99±0.31\right)×{10}^{-3}$. In addition, the upper limit on the branching fraction of the doubly Cabbibo-suppressed decay ${\Lambda }_{c}^{+}\to n{K}^{+}{\pi }^{0}$ is $7.1×{10}^{-4}$ at the 90% confidence level. The upper limits on the branching fractions of ${\Lambda }_{c}^{+}\to {\Sigma }^{0}{K}^{+}{\pi }^{0}$ and $\Lambda {K}^{+}{\pi }^{0}$ are also determined to be $1.8×{10}^{-3}$ and $2.0×{10}^{-3}$, respectively.