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We study a radiative $p^{15}$N capture on the ground state of $^{16}$O atstellar energies within the framework of a modified potential cluster model(MPCM) with forbidden states, including low lying resonances. The investigationof the $^{15}$N($p,\gamma $)$^{16}$O reaction includes the consideration of$^{3}S_{1}$ resonances due to $E1$ transitions and contribution of $^{3}P_{1}$scattering wave in $p$ + $^{15}$N channel due to $^{3}P_{1}\longrightarrow $$^{3}P_{0}$ $M1$ transition. We calculate the astrophysical low-energy$S-$factor and extrapolated $S(0)$ turned out to be within $34.7-40.4$keV$\cdot $b. It is elucidated the important role of the asymptotic constant(AC) for the $^{15}$N($p,\gamma $)$^{16}$O process with interfering$^{3}S_{1}$(312) and $^{3}S_{1}$(962) resonances. A comparison of ourcalculation for $S-$factor with existing experimental and theoretical data isaddressed and the reasonable agreement is found.  The reaction rate is calculated and compared with the existing rates. It hasnegligible dependence on the variation of AC, but shows strong impact of theinterference of $^{3}S_{1}$(312) and $^{3}S_{1}$(962) resonances, especially at$T_{9}$ referring to the CNO Gamow windows. We present a stellar temperaturedependence on the Gamow energy and a comparison of rates for radiative protoncapture reactions for CNO cycle on nitrogen isotopes obtained in the frameworkof the MPCM and give temperature windows, prevalence, and significance of eachprocess.

The astrophysical $S-$factor and reaction rate for $^{15}$N($p,\gamma$)$^{16}$O within the modified potential cluster model