We report a large mode area (LMA), Ge11.5As24Se64.5 six-fold symmetry quasi-periodic dual cladding leakage channel fiber (LCF) for supercontinuum generation (SCG) from 2 to $15~\mu \text{m}$ wavelengths. The proposed LMA fiber exhibits single-mode behavior by means of higher order mode delocalization for the entire wavelengths. Besides, the LCF possesses two zero dispersion wavelengths at 4.36 and $14.16~\mu \text{m}$ . Indeed, we numerically demonstrated the spectral broadening of continuum for the first time from 2 to $15~\mu \text{m}$ in the quasi-periodic dual cladding LCF for a length of 10 mm. It is observed that the red-shifted soliton at the centre wavelength of $9.42~\mu \text{m}$ obtain an energy of 0.164 nJ for a low input energy of 0.2 nJ. Further, the SCG in the proposed LCF attains a high conversion efficiency of 82 % at the solitonic spectrum and broadest spanning from 2 to $15~\mu \text{m}$ for the low input energy of 0.2 nJ. Thus, the proposed LCF-based SC source is the best choice for the applications, such as optical sensing, optical communication, food quality monitoring, and early cancer diagnostics.