  We define an involutive version of Khovanov homology and a pair of
integer-valued invariants $(\underline{s}, \bar{s})$ for strongly invertible
knots, which is an equivariant version of the Rasmussen invariant $s$. Using
these invariants, we show that there is an infinite family of knots $J_n$
admitting exotic pairs of slice disks. Our construction is intended to give a
Khovanov-theoretic analogue of the formalism given by Dai, Mallick and
Stoffregen in knot Floer theory.
