  L1521F is found to be forming multiple cores and it is cited as an example of
the densest core with an embedded VeLLO in a highly dynamical environment. We
present the core-scale magnetic fields (B-fields) in the near vicinity of the
VeLLO L1521F-IRS using submm polarization measurements at 850$~\mu$m using JCMT
POL-2. This is the first attempt to use high-sensitivity observations to map
the sub-parsec scale B-fields in a core with a VeLLO. The B-fields are ordered
and very well connected to the parsec-scale field geometry seen in our earlier
optical polarization observations and the large-scale structure seen in Planck
dust polarization. The core scale B-field strength estimated using
Davis-Chandrasekhar-Fermi relation is $\rm 330\pm100~\mu$G which is more than
ten times of the value we obtained in the envelope (envelope in this paper is
"core envelope"). This indicates that B-fields are getting stronger on smaller
scales. The magnetic energies are found to be 1 to 2 orders of magnitude higher
than non-thermal kinetic energies in the envelope and core. This suggests that
magnetic fields are more important than turbulence in the energy budget of
L1521F. The mass-to-flux ratio of 2.3$\pm$0.7 suggests that the core is
magnetically-supercritical. The degree of polarization is steadily decreasing
towards the denser part of the core with a power law slope of -0.86.
