We have delved into the phenomenon of high-order harmonic generation within a helium atom under the influence of a plasmon-assisted shaping pulse in this investigation. Our findings reveal an intriguing manipulation of the frequency peak position in the harmonic emission by adjusting the absolute phase parameter within the frequency domain of the shaping pulse. This phenomenon holds potential significance for experimental setups necessitating precisely tuned single harmonics. Notably, we have observed a modulated shift in the created harmonic photon energy, spanning an impressive range of 1.2 eV. This frequency peak shift is rooted in the asymmetry exhibited by the rising and falling edges of the laser pulse, directly influencing the position of the peak frequency emission. Our study quantifies the dependence of this tuning range and the asymmetry of the laser pulse, offering valuable insights into the underlying mechanisms driving this phenomenon. Furthermore, our investigation uncovers the emergence of semi-integer order harmonics as the phase parameter is altered. We attribute this discovery to the intricate interference between harmonics generated by the primary and secondary return cores. This observation introduces an innovative approach for generating semi-integer order harmonics, thus expanding our understanding of high-order harmonic generation. Ultimately, our work contributes to the broader comprehension of complex phenomena in laser-matter interactions and provides a foundation for harnessing these effects in various applications, particularly those involving precise spectral control and the generation of unique harmonic patterns.