One of the unsolved problems in cosmic ray (CR) physics is the determination of sources and acceleration mechanism(s) of Galactic ( E less than or similar to 10(18)) eV and extragalactic ( E greater than or similar to 10(17) eV) CR. Ultra high energy CR (UHECR, E > 10(18) eV) are believed to be of extragalactic origin, but some contribution from transient Galactic sources is possible. So, magnetar wind nebulae (MWNe), created by newborn millisecond magnetars, and magnetar giant flares are PeVatron candidates and even potential sources of UHECR. Promising signature of effective acceleration processes in magnetars' neighbourhoods should be nonthermal high-energy and very high-energy gamma-ray emission due to pp collisions with a subsequent pion decay (hadronic scenario) and inverse Compton scattering of low energy background photons by ultrarelativistic electrons and positrons (leptonic scenario). In this work we explain the HE and VHE gamma-ray emission from the vicinity of the magnetar SGR 1900+14 - potential Galactic source of E 10(20) eV triplet - by the hadronic and leptonic emission of cosmic rays accelerated in a magnetar-related Supernova remnant (SNR) and/or MWN. To this end we have carried out a simulation of the observed HE and VHE gamma-ray emission, spatially coincident with the magnetar SGR 1900+14. The extended Fermi-LAT source 4FGL J1908.6+0915e, the extended H.E.S.S. source candidate HOTS J1907+091 and the point-like HAWC TeVsource3HWC J1907+085were considered. We showthat the observed gamma-ray emission from the magnetar SGR 1900+14 outskirts can be explained by a (still undetected) magnetar-connected super-luminous Supernova (Hypernova) remnant and/or a MWN created by newborn millisecond magnetar with a large initial rotational energy E-rot similar to 10(52) erg.