The electron capture process in N⁷⁺ + H (1s) collisions in a plasma environment is systematically investigated using the two-center atomic orbital close-coupling method and the Debye screening potential, for collision energies ranging from 0.5 to 200 keV/u. The results indicate that for collision energies below approximately 5 keV/u, the cross section for capture into the 4l states first increases and then decreases as the screening length decreases. This non-monotonic behavior arises because enhanced screening strength reduces the energy gap between the initial and final states, thereby enlarging the region of strong interaction, and at lower collision energies, the system resides in this interaction region for a longer duration, leading to an increased transition probability. In contrast, the energy differences for the 5l states change only slightly with increasing screening strength, and its cross section exhibits a monotonic decline under the screening effect. Consequently, as screening intensifies, the dominant capture channel shifts from n=5 to n=4. By comparing the present results with previous studies on C⁶⁺ + H (Z=6) and O⁸⁺ + H (Z= 8) systems, a systematic trend emerges: as the projectile nuclear charge Z increases, the dominant capture channel in the unscreened case moves to higher principal quantum numbers n, whereas the plasma screening effect tends to enhance the lower-n channels. The N⁷⁺ system (Z=7) lies exactly in the critical region where these two competing factors cross, which explains why the dominant channel switching is observed in this system. In addition, the effect of plasma screening on charge exchange spectral lines is investigated. Compared with the unscreened case, all spectral lines are redshifted, and the redshift magnitude increases with decreasing screening length. The spectral line intensities exhibit a clear dependence on collision energy as the screening length varies: at lower collision energies, the enhancement of the n=4 capture cross section dominates, and the intensities of low-n spectral lines increase with increasing screening strength; at higher collision energies, this enhancement weakens, and only the n=4 spectral lines show a slight increase in intensity. This work reveals the modulation mechanism of the plasma screening effect on the competition among different capture channels in asymmetric collision systems, and the findings provide a theoretical basis for charge exchange spectroscopic diagnostics in related fields.