Context. In our previous work we found a statistically significant offset ΔV ≈ 27 m s −1 between the radial velocities of the HC 3 N J = 2−1 and NH 3 (J, K) = (1, 1) transitions observed in molecular cores from the Milky Way. This may indicate that the electron-toproton mass ratio, μ ≡ m e /m p , increases by ∼3 × 10 −8 when measured under interstellar conditions with matter densities of more than 10 orders of magnitude lower than with laboratory (terrestrial) environments. Aims. We map four molecular cores L1498, L1512, L1517, and L1400K selected from our previous sample to estimate systematic effects in ΔV due to possible velocity gradients or other sources across the cloud and to check the reproducibility of the velocity offsets on the year-to-year time base. Methods. We use the ammonia method, which involves observations of inversion lines of NH 3 complemented by rotational lines of other molecular species and allows us to test changes in μ caused by a higher sensitivity of the inversion frequencies to the μ-variation than with the rotational frequencies. Results. We find that in two cores L1498 and L1512 the NH 3 (1, 1) and HC 3 N (2-1) transitions closely trace the same material and show an offset of ΔV ≡ V lsr (HC 3 N) -V lsr (NH 3 ) = 26.9 ± 1.2 stat ± 3.0 sys m s −1 throughout the entire clouds. The offsets measured in L1517B and L1400K are 46.9 ± 3.3 stat ± 3.0 sys m s −1 and 8.5 ± 3.4 stat ± 3.0 sys m s −1 , respectively, and are, probably, subject to Doppler shifts due to spatial segregation of HC 3 N versus NH 3 . We also determine frequency shifts caused by external electric and magnetic fields and by the cosmic black body radiation-induced Stark effect and find that they are less than 1 m s −1 . Conclusions. The measured velocity offset in L1498 and L1512, when interpreted in terms of Δμ/μ ≡ (μ obs − μ lab )/μ lab , gives Δμ/μ = (26 ± 1 stat ± 3 sys ) × 10 −9 . Although this estimate is based on a limited number of sources and molecular pairs used in the ammonia method, it demonstrates a high accuracy with which the fundamental physics can be tested by means of radio observations. The non-zero signal in Δμ/μ should be further examined as larger and more accurate data sets become available.