Phase RNum{2} of the LAMOST-{sl Kepler/K}2 survey (LK-MRS), initiated in 2018, aims at collecting medium-resolution spectra ($Rsim7,500$; hereafter MRS) for more than $50,000$ stars with multiple visits ($sim60$ epochs) over a period of 5 years (2018 September to 2023 June). We selected 20 footprints distributed across the {sl Kepler} field and six {sl K}2 campaigns, with each plate containing a number of stars ranging from $sim2,000$ to $sim 3,000$. During the first year of observations, the LK-MRS has already collected $sim280,000$ and $sim369,000$ high-quality spectra in the blue and red wavelength range, respectively. The atmospheric parameters and radial velocities for $sim259,000$ spectra of $21,053$ targets were successfully calculated by the LASP pipeline. The internal uncertainties for the effective temperature, surface gravity, metallicity, and radial velocity are found to be $100$,K, $0.15$,dex, $0.09$,dex, and $1.00$,km,s$^{-1}$, respectively. We found $14,997$, $20,091$, and $1,514$ stars in common with the targets from the LAMOST low-resolution survey (LRS), GAIA and APOGEE, respectively, corresponding to a fraction of $sim70%$, $sim95%$ and $sim7.2%$. In general, the parameters derived from LK-MRS spectra are consistent with those obtained from the LRS and APOGEE spectra, but the scatter increases as the surface gravity decreases when comparing with the measurements from APOGEE. A large discrepancy is found with the GAIA values of the effective temperature. The comparisons of radial velocities of LK-MRS to GAIA and LK-MRS to APOGEE nearly follow an Gaussian distribution with a mean $musim1.10$ and $0.73$,km,s$^{-1}$, respectively.
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