Phase II of the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST)-Kepler/K2 survey (LK-MRS), initiated in 2018, aims at collecting medium-resolution spectra (R~7500; hereafter MRS) for more than 50000 stars with multiple visits (~60 epochs) over a period of 5yr (2018 September to 2023 June). We selected 20 footprints distributed across the Kepler field and six K2 campaigns, with each plate containing a number of stars ranging from ~2000 to ~3000. During the first year of observations, the LK-MRS has already visited 13 plates 223 times over 40 individual nights, and collected ~280000 and ~369000 high-quality spectra in the blue and red wavelength ranges, respectively. The atmospheric parameters and radial velocities for ~259000 spectra of 21053 targets were successfully calculated by the LAMOST stellar parameter pipeline. The internal uncertainties for the effective temperature, surface gravity, metallicity, and radial velocity are found to be 100K, 0.15dex, 0.09dex, and 1.00km/s, respectively, when derived from a medium-resolution LAMOST spectrum with a signal-to-noise ratio (S/N) in the g band of 10. All of the uncertainties decrease as S/N increases, but they stabilize for S/N>100. We found 14997, 20091, and 1514 stars in common with the targets from the LAMOST low-resolution survey (LRS), Gaia, and the Apache Point Observatory Galactic Evolution Experiment (APOGEE), respectively, corresponding to fractions of ~70%, ~95%, and ~7.2%. 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. Comparisons of the radial velocities of LK-MRS to Gaia and LK-MRS to APOGEE nearly follow a Gaussian distribution with means of {mu}~1.10 and 0.73km/s, respectively. We expect that the results from the LK-MRS spectra will shed new light on binary stars, asteroseismology, stellar activity, and other research fields.