Context. The Lyα emission is an important tracer of neutral gas in a circum-galactic medium (CGM) around high-z quasi-stellar objects (QSOs). The origin of Lyα emission around QSOs is still under debate, bringing on significant implications for galaxy formation and evolution. Aims. In this paper, we study Lyα 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 All-wavelength Extended Groth Strip International Survey (AEGIS) field. Methods. Using the contiguous narrow-band (NB) images from the miniJPAS survey and Sloan Digital Sky Survey (SDSS) spectra, we analyzed their morphology, nature, and origin. Results. We report the serendipitous detection of double-core Lyα morphology around two QSOs, which is rarely seen among other QSOs. The separations of the two Lyα cores are 11.07 ± 2.26 kpcs (1.47 ± 0.3″) and 9.73 ± 1.55 kpcs (1.31 ± 0.21″), with Lyα line luminosities of ∼3.35 × 1044 erg s−1 and ∼6.99 × 1044 erg s −1 for QSO1 and QSO2, respectively. The miniJPAS NB images show evidence of extended Lyα and CIV morphology for both QSOs and extended HeII morphology for QSO1. Conclusions. 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 Lyα luminosities. We suggest that galactic outflows are the major powering mechanism for the double-core Lyα morphology. Considering the relatively shallow exposures of miniJPAS, the objects found here could merely form the cusp of a promising number of such objects that will be uncovered in the upcoming full Javalambre-Physics of the Accelerated Universe Astrophysical Survey (J-PAS) survey and deep integral field units (IFU) observations with 8–10 m telescopes will be essential for constraining the underlying physical mechanism that is responsible for the double-cored morphology.