  As a new ingredient for analyzing the fine structure of entanglement, we
study the symmetry resolution of the modular flow of $U(1)$-invariant operators
in theories endowed with a global $U(1)$ symmetry. We provide a consistent
definition of symmetry-resolved modular flow that is defined for a local
algebra of operators associated to a sector with fixed charge. We also discuss
the symmetry-resolved modular correlation functions and show that they satisfy
the KMS condition in each symmetry sector. Our analysis relies on the
factorization of the Hilbert space associated to spatial subsystems. We provide
a toolkit for computing the symmetry-resolved modular correlation function of
the charge density operator in free fermionic theories. As an application, we
compute this correlation function for a $1+1$-dimensional free massless Dirac
field theory and find that it is independent of the charge sector at leading
order in the ultraviolet cutoff expansion. This feature can be regarded as a
charge equipartition of the modular correlation function. Although obtained for
free fermions, these results may be of potential interest for bulk
reconstruction in AdS/CFT.
