  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.
