An accurate knowledge of nuclear parton distribution functions (nPDFs) is an essential ingredient of high energy physics calculations when the processes are involving nuclei in the initial state. It is well known now that the prompt photon production both in hadronic and nuclear collisions is a powerful tool for exploring the parton densities in the nucleon and nuclei especially of the gluon. In this work, we are going to perform a comprehensive study of the isolated prompt photon production in p-Pb collisions at backward rapidities to find the best kinematic regions in which the experimental measurements have most sensitivity to the nuclear modifications of parton densities.Most emphasis will be placed on the antishadowing nuclear modification. To this aim, we calculate and compare various quantities at different values of center-of-mass energy covered by the LHC and also different rapidity regions to realize which one is most useful.Besides the parton distribution functions (PDFs), whether unpolarized [1][2][3][4][5][6][7][8][9][10][11] or polarized [12][13][14][15][16][17][18], and fragmentation functions (FFs) [19][20][21][22][23], the nuclear modifications of PDFs [24][25][26][27][28][29][30][31] are also important ingredients of high energy physics calculations, in particular, for processes involving nuclei in the initial state. In fact, without having nuclear PDFs (nPDFs) which describe the structure of the colliding nuclei, the theoretical calculation of the cross sections in any nuclear collision will not be possible. Thanks to the collinear factorization theorem [32,33], the nPDFs can be extracted just in a way similar to the PDFs determination through a global analysis of nuclear experimental data. Nowadays, due to many developments achieved in the phenomenological approaches, theoretical calculations and experimental measurements, the PDFs are well determined in a wide range of the momentum fraction x. However, the situation is not very satisfying for the case of nPDFs because of the lack of experimental data.Although the main experimental data for constraining nPDFs come from the old fixedtarget deep inelastic scattering (DIS) and proton-nucleus Drell-Yan (DY) dilepton production experiments, there are some analyses in which the neutrino DIS data have also been used [25,27,30]. Furthermore, the inclusive pion production from d-Au collisions at RHIC that can be considered as another source to put further constraints on the nuclear gluon distribution is usually used in the nPDFs analyses [26][27][28]30]. Recently, EPPS16 [30] has also included, for the first time, the fixed-target DY data in pion-nucleus collisions and new LHC proton-lead (p-Pb) data on dijet and heavy gauge-boson production. There are also some studies show that important information about nPDFs can be achieved by analyzing the prompt photon production in nuclear collisions [34][35][36][37][38][39], jet and dijet photoproduction measurements at a future electron-ion collider (EIC) [40,41], single inclusive jet production at very forwa...