Abstract: This is the second lecture about SYZ and topological mirror symmetries for parabolic Hitchin systems in type B/C. One of the key step to establish mirror symmetries for Hitchin systems is to understand the generic fibers of the Hitchin map, and the most powerful tool is the so called BNR correspondence which relates Higgs bundles to rank one sheaves on the spectral curves. However, in parabolic case, the spectral curves usually have singularities, which may cause many difficulties but also many interesting phenomena. In this talk, I will focus on the formal disk around the singular point, and define the notion of local Higgs bundles, which can be seem as not only the restriction of parabolic Higgs bundle to the formal disk but also an infinitesimal enhancement of nilpotent Lie algebra elements. The main results in this part are some decomposition theorems of the local Higgs bundles in type B/C. As a byproduct, we found a new geometric interpretation of the Lusztig’s canonical quotient(arXiv:2403.07552).