Context. New space missions, such as NASA TESS or ESA PLATO, will focus on bright stars, which have been largely ignored by modern large surveys, especially in the northern sky. Spectroscopic information is of paramount importance in characterising the stars and analysing planets possibly orbiting them, and in studying the Galactic disc evolution. Aims. The aim of this work was to analyse all bright (V < 8 mag) F, G, and K dwarf stars using high-resolution spectra in the selected sky fields near the northern celestial pole. Methods. The observations were carried out with the 1.65 m diameter telescope at the Molėtai Astronomical Observatory and a fibre-fed high-resolution spectrograph covering a full visible wavelength range (4000–8500 Å). The atmospheric parameters were derived using the classical equivalent width approach while the individual chemical element abundances were determined from spectral synthesis. For both tasks the one-dimensional plane-parallel LTE MARCS stellar model atmospheres were applied. The NLTE effects for the majority of elemental abundances in our sample were negligible; however, we did calculate the NLTE corrections for the potassium abundances, as they were determined from the large 7698.9 Å line. For manganese and copper we have accounted for a hyperfine splitting. Results. We determined the main atmospheric parameters, kinematic properties, orbital parameters, and stellar ages for 109 newly observed stars and chemical abundances of Na I, Mg I, Al I, Si I, Si II, S I, K I, Ca I, Ca II, Sc I, Sc II, Ti I, Ti II, V I, Cr I, Cr II, Mn I, Fe I, Fe II, Co I, Ni I, Cu I, and Zn I for 249 F, G, and K dwarf stars observed in the present study and in our previous study. The [Mg I/Fe I] ratio was adopted to define the thin-disc (α-poor) and thick-disc (α-rich) stars in our sample. We explored the behaviour of 21 chemical species in the [El/Fe I] versus [Fe I/H] and [El/Fe I] versus age planes, and compared the results with the latest Galactic chemical evolution models. We also explored [El/Fe I] gradients according to the mean Galactocentric distances and maximum height above the Galactic plane. Conclusions. We found that in the Galactic thin-disc [El/Fe I] ratios of α-elements and aluminium have a positive trend with respect to age while the trend of Mn is clearly negative. Abundances of other species do not display significant trends. While the current theoretical models are able to reproduce the generic trends of the elements, they often seem to overestimate or underestimate the observational abundances. We found that the α-element and zinc abundances have slightly positive or flat radial and vertical gradients, while gradients for the odd-Z element Na, K, V, and Mn abundances are negative.