Higher order dispersion (HOD) parameters play an important role in the overall performance of fiber optic parametric amplifier (FOPA). Effect of HOD parameters on gain spectrum and bandwidth for an engineered dispersion profile has been investigated revealing some interesting outcomes. Here, we have optimized a near-zero ultra flat dispersion profile around the communication wavelength based on selective liquid infiltration technique. The performance of FOPA in terms of gain and bandwidth based on the optimized dispersion profile is thoroughly investigated incorporating different HOD parameters. Considering upto 6th order of HOD terms, we could observe one additional sharp gain peak (on both sides of the central gain maxima) which otherwise is absent when considering other lesser values of HOD parameters. The spectral shift and width of the additional peaks are found to vary significantly due to the incorporation of these different HOD terms. The effect of HOD parameters are found to be extremely significant for the generation of new frequencies as well as modification of the peak widths for the communication band application.