39 K atoms have the smallest ground state ( 2 S 1/2 ) hyperfine splitting of all the most naturally abundent alkali isotopes and, consequently, the smallest characteristic magnetic field value B0 = A2 S 1/2 /µB ≈ 170 G, where A2 S 1/2 is the ground state's magnetic dipole interaction constant. In the hyperfine Paschen-Back regime (B ≫ B0, where B is the magnitude of the external magnetic field applied on the atoms), only 8 Zeeman transitions are visible in the absorption spectrum of the D1 line of 39 K, while the probabilities of the remaining 16 Zeeman transitions tend to zero. In the case of 39 K, this behavior is reached already at relatively low magnetic field B > B0. For each circular polarization (σ − , σ + ), 4 spectrally resolved atomic transitions having a sub-Doppler width are recorded using a sub-microsized vapor cell of thickness L = 120 − 390 nm. We present a method that allows to measure the magnetic field in the range 0.1−10 kG with micrometer spatial resolution, which is relevant in particular for the determination of magnetic fields with a large gradient (up to 3 G/µm). The theoretical model describes well the experimental results.