  B-fields are predicted to play a role in the formation of filamentary
structures and their fragmentation process. We aim at investigating the role of
the B-field in the process of core fragmentation toward the hub-filament
systems in the IRDC G14.2, which present different fragmentation level. We
performed observations of the thermal dust polarization at 350 {\mu}m using the
CSO toward the hubs. We applied the polarization--intensity-gradient method to
estimate the significance of the B-field over the G-force. The B-field in Hub-N
shows a uniform structure along the E-W orientation, perpendicular to the major
axis of the hub-filament system. The I-gradient in Hub-N displays a local
minimum coinciding with the dust core MM1a detected with interferometric
observations. The B-field orientation is perturbed when approaching the dust
core. Hub-S shows 2 local minima, reflecting the bimodal distribution of the
B-field. In Hub-N, both E and W of the hub-filament system, the I-gradient and
the B-field are parallel whereas they tend to be perpendicular when penetrating
the filaments and hub. The analysis of the {\delta}- and {\Sigma} B-maps
indicate that, the B-field cannot prevent the collapse, suggesting that the
B-field is initially dragged by the infalling motion and aligned with it, or is
channeling material toward the central ridge from both sides. Values of
{\Sigma} B > 1 are found toward a N-S ridge encompassing the dust emission
peak, indicating that in this region B-field dominates over G-force, or that
with the current angular resolution we cannot resolve an hypothetical more
complex structure. We estimated the B-field strength, the MtF ratio and the A-M
number, and found differences between the 2 hubs. The different levels of
fragmentation observed in these 2 hubs could arise from the differences in the
B-field properties rather than from different intensity of the G-field.
