  In this paper, we introduce and study relative phantom morphisms in
extriangulated categories defined by Nakaoka and Palu. Then using their
properties, we show that if $(\C,\E,\s)$ is an extriangulated category with
enough injective objects and projective objects, then there exists a bijective
correspondence between any two of the following classes: (1) special
precovering ideals of $\C$; (2) special preenveloping ideals of $\C$; (3)
additive subfunctors of $\E$ having enough special injective morphisms; and (4)
additive subfunctors of $\E$ having enough special projective morphisms.
Moreover, we show that if $(\C,\E,\s)$ is an extriangulated category with
enough injective objects and projective morphisms, then there exists a
bijective correspondence between the following two classes: (1) all
object-special precovering ideals of $\C$; (2) all additive subfunctors of $\E$
having enough special injective objects.
