  Higher homological algebra, basically done in the framework of an $n$-cluster
tilting subcategory $\mathcal{M}$ of an abelian category $\mathcal{A}$, has
been the topic of several recent researches. In this paper, we study a relative
version, in the sense of Auslander-Solberg, of the higher homological algebra.
To this end, we consider an additive sub-bifunctor $F$ of
$\mathrm{Ext}^n_{\mathcal{M}}( -,-)$ as the basis of our relative theory. This,
in turn, specifies a collection of $n$-exact sequences in $\mathcal{M}$, which
allows us to delve into the relative higher homological algebra. Our results
include a proof of the relative $n$-Auslander-Reiten duality formula, as well
as an exploration of relative Grothendieck groups, among other results. As an
application, we provide necessary and sufficient conditions for $\mathcal{M}$
to be of finite type.
