Composite field

In quantum field theory, a composite field is a field defined in terms of other more "elementary" fields. It might describe a composite particle or it might not.
It might be local, or it might be nonlocal. However, "quantum fields do not exist as a point taken in isolation," so "local" does not mean literally a single point.
Composite fields use a very specific kind of statistics, called "duality and arbitrary statistics".
Under Noether's theorem, Noether fields are often composite fields, and they are local.
In the generalized LSZ formalism, composite fields, which are usually nonlocal, are used to model asymptotic bound states.