Supernova remnants (SNRs), star formation regions (SFRs), and pulsar wind nebulae (PWNe) are prime candidates for Galactic PeVatrons. The nonthermal high-energy (HE, $\varepsilon>100 \textrm{ MeV}$) and very high-energy (VHE, $\varepsilon>100 \textrm{ GeV}$) $\gamma$-ray emission from these sources should be a promising manifestation of acceleration processes. We investigate the possibility to explain the HE and VHE $\gamma$-ray emission from the sky region of the magnetar SGR 1900+14 as a signature of cosmic rays accelerated in above mentioned sources. To this end, we simulate the $\gamma$-ray emission from the extended Fermi-LAT HE source 4FGL J1908.6+0915e, the extended VHE H.E.S.S. source candidate HOTS J1907+091, and the point-like HAWC TeV source 3HWC J1907+085, which are spatially coincident with the SNR G42.8+0.6, the magnetar SGR 1900+14 and the star forming region W49A. The simulations are performed within the hadronic and leptonic models. We show that the observed $\gamma$-ray emission from the region of the magnetar SGR 1900+14 can, in principle, include contributions of different intensities from all three types of (potentially confused) sources. The considered in detail cases of a magnetar-connected but still undetected SNR and a PWN are the most promising ones, but with a serious requirement on the energy reserve of radiated CR particles - of order of $10^{51}d_{\textrm{10kpc}}^{2}$ erg for sources at a distance of $d\sim 10$ kpc. Such energy reserve can be provided by the magnetar-related Hypernova and/or magnetar wind nebula remnant created by the newborn millisecond magnetar with the large supply of rotational energy $E_{\textrm{rot}}\sim 10^{52}\textrm{ erg}$.
Comment: 13 pages, 7 figures; version 2: paper was significantly revised and rewritten following comments from the referee, matches the version accepted for publication in MNRAS