  We carry out a bootstrap study of four-point correlators in 4d
$\mathcal{N}=2$ SCFTs which are dual to super Yang-Mills on $AdS_5\times S^3$.
We focus on the simplest $\frac{1}{2}$-BPS operators which correspond to the
super gluons in the massless current multiplet. Our computation is based on an
ansatz in position space which is inspired by a hidden symmetry structure
manifest in the leading terms of the Lorentzian singularities of the
correlators. By using other consistency conditions, we completely fix the super
gluon correlators at one and two loops in the bulk genus expansion, up to
possible counterterms. Our results reveal a number of interesting properties
enriched by the color structures. In particular, the implication of hidden
conformal symmetry on the full super gluon reduced correlator exhibits an
analogous pattern as in the $AdS_5\times S^5$ supergravity correlators recently
computed up to two loops.
