Supernova remnants (SNRs), star formation regions (SFRs), and pulsar wind nebulae (PWNe) are prime candidates for Galactic PeVatrons. The nonthermal high-energy (HE, ϵ > 100 MeV) and very high-energy (VHE, ϵ > 100 GeV) γ-ray emission from these sources should be a promising manifestation of acceleration processes. We investigate the possibility to explain the HE and VHE γ-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 γ-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 γ-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 ∼ 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 Erot ∼ 1052 erg.