  All standard measures of bipartite entanglement in one-dimensional quantum
field theories can be expressed in terms of correlators of branch point twist
fields, here denoted by $\mathcal{T}$ and $\mathcal{T}^\dagger$. These are
symmetry fields associated to cyclic permutation symmetry in a replica theory
and having the smallest conformal dimension at the critical point. Recently,
other twist fields (composite twist fields), typically of higher dimension,
have been shown to play a role in the study of a new measure of entanglement
known as the symmetry resolved entanglement entropy. In this paper we give an
exact expression for the two-point function of a composite twist field that
arises in the Ising field theory. In doing so we extend the techniques
originally developed for the standard branch point twist field in free theories
as well as an existing computation due to Horv\'ath and Calabrese of the same
two-point function which focused on the leading large-distance contribution. We
study the ground state two-point function of the composite twist field
$\mathcal{T}_\mu$ and its conjugate $\mathcal{T}_\mu^\dagger$. At criticality,
this field can be defined as the leading field in the operator product
expansion of $\mathcal{T}$ and the disorder field $\mu$. We find a general
formula for $\log \langle \mathcal{T}_\mu(0) \mathcal{T}^\dagger_\mu(r)\rangle$
and for (the derivative of) its analytic continuation to positive real replica
numbers greater than 1. We check our formula for consistency by showing that at
short distances it exactly reproduces the expected conformal dimension
