We analyze the effect of the additional repulsive core on the ground state energy of the off-axis neutral donor in GaAs/Ga1-xAlxAs cylindrical nanotube in the presence of the uniform magnetic field applied along the symmetry axis by using the recently developed fractal dimension method. Curves of the D^0 ground state binding energies as a function of the donor distance from the axis and density states with randomly distributed donors show that the additional peaks in the curves of the density of impurity states appear due to the presence of the additional repulsive core in the middle's well. To take into account the mixing of the low lying subbands we express the wave function as a product of the combination of 1s and 2px,y wave functions with an unknown envelope function that depends only on electron-ion separation.