The aim of this work is to determine abundances of neutron-capture elements for thin- and thick-disc F, G, and K stars in several selected sky fields near the North Ecliptic Pole and to compare the results with the Galactic chemical evolution models, to explore elemental gradients according to stellar ages, mean galactocentric distances, and maximum heights above the Galactic plane. The observational data were obtained with the 1.65 meter telescope at the Moletai Astronomical Observatory and a fibre-fed high-resolution spectrograph covering a full visible wavelength range (4000-8500{AA}). Elemental abundances were determined using a differential line-by-line spectrum synthesis using the TURBOSPECTRUM code with the MARCS stellar model atmospheres and accounting for the hyperfine-structure effects. Results. We determined abundances of Sr, Y, Zr, Ba, La, Ce, Pr, Nd, Sm, and Eu for 424 thin- and 82 thick-disc stars. The sample of thick-disc stars shows a clearly visible decrease of [Eu/Mg] with increasing metallicity compared to the thin-disc stars, bringing more evidences of different chemical evolution in these two Galactic components. Abundance correlation with age slopes for the investigated thin-disc stars are slightly negative for the majority of s-process dominated elements, while r-process dominated elements have positive correlations. Our sample of thin-disc stars with ages spanning from 0.1 to 9Gyrs gives the [Y/Mg]=0.022(+/-0.015)-0.027(+/-0.003)/age[Gyr] relation. However, for the thick-disc stars, when taking into account also data from other studies, we found that [Y/Mg] cannot serve as an age indicator. The radial abundance-to-iron gradients in the thin disc are negligible for the s-process dominated elements and become positive for the r-process dominated elements, the vertical gradients are negative for the light s-process dominated elements and become positive for the r-process dominated elements. In the thick disc, the radial abundance-to-iron slopes are negligible and the vertical ones are predominantly negative.