  We study the compactification of 4D $\mathcal{N}=3$ superconformal field
theories (SCFTs) on $S^1$, focusing on the relation between the 4D
superconformal index and 3D partition function on the squashed sphere $S^3_b$.
Since the center $\mathfrak{u}(1)$ of the $\mathfrak{u}(3)$ R-symmetry of the
4D theory can mix with an $\mathcal{N}=6$ abelian flavor symmetry in three
dimensions, the precise 4D/3D relation for the global symmetry is not obvious.
Focusing on the case in which the 3D theory is the ABJM theory, we demonstrate
that the above R-symmetry mixing can be precisely identified by considering the
Schur limit (and/or its $\mathcal{N}=3$ cousin) of the 4D index. As a result,
we generalize to the ABJM theories recent discussions on the connection between
supersymmetry enhancement of the 4D index and squashing independence of the
$S^3_b$ partition function.
