  We find boundary confining dualities of 3d $\mathcal{N}=2$ supersymmetric
gauge theories with exceptional gauge groups. The half-indices which enumerate
the boundary BPS local operators in the presence of Neumann and Dirichlet
boundary conditions for gauge fields are identified with the Askey-Wilson type
$q$-beta integrals and Macdonald type sums respectively. New conjectural
identities of $E_6$ and $E_7$ integrals and sums are derived from the boundary
confining dualities. We also consider theories with a vector multiplet and
adjoint chiral, which correspond to an $\mathcal{N}=4$ vector multiplet, with
appropriate boundary conditions. We argue for the boundary confinement of the
$\mathcal{N}=4$ vector multiplet and comment on such theories also with
classical gauge groups.
