The Ly$\alpha$ emission is an important tracer of neutral gas in a circum-galactic medium (CGM) around high-z QSOs. The origin of Lya emission around QSOs is still under debate which has significant implications for galaxy formation and evolution. In this paper, we study Ly$\alpha$ nebulae around two high redshift QSOs, SDSS J141935.58+525710.7 at $z=3.218$ (hereafter QSO1) and SDSS J141813.40+525240.4 at $z=3.287$ (hereafter QSO2), from the miniJPAS survey within the AEGIS field. Using the contiguous narrow-band (NB) images from the miniJPAS survey and SDSS spectra, we analyzed their morphology, nature, and origin. We report the serendipitous detection of double-core Ly\al\ morphology around two QSOs which is rarely seen among other QSOs. The separations of the two Ly\al~cores are 11.07 $\pm$ 2.26 kpcs (1.47 $\pm$ 0.3$^{\prime\prime}$) and 9.73 $\pm$ 1.55 kpcs (1.31 $\pm$ 0.21$^{\prime\prime}$) with Ly$\alpha$~line luminosities of $\sim$ 3.35 $\times 10^{44}$ erg s $^{-1} $ and $\sim$ 6.99 $\times$ 10$^{44}$ erg s $^{-1}$ for QSO1 and QSO2, respectively. The miniJPAS NB images show evidence of extended Ly$\alpha$ and CIV morphology for both QSOs and extended HeII morphology for QSO1. These two QSOs may be potential candidates for the new enormous Lyman alpha nebula (ELAN) found from the miniJPAS survey due to their extended morphology in the shallow depth and relatively high Ly$\alpha$ luminosities. We suggest that galactic outflows are the major powering mechanism for the double-core Ly$\alpha$ morphology. Considering the relatively shallow exposures of miniJPAS, the objects found here could be the tip of the iceberg of a promising number of such objects that will be uncovered in the upcoming full J-PAS survey and deep IFU observations with 8-10m telescopes will be essential for constraining the underlying physical mechanism that is responsible for the double-cored morphology.