  We define an operation on homology ${B}^4$ which we call an $n$-twist annulus
modification. We give a new construction of smoothly slice knots and exotically
slice knots via $n$-twist annulus modifications. As an application, we present
a new example of a smoothly slice knot with non-slice derivatives. Such
examples were first discovered by Cochran and Davis. Also, we relate $n$-twist
annulus modifications to $n$-fold annulus twists which was first introduced by
Osoinach, then has been used by Abe and Tange to construct smoothly slice
knots. Furthermore we consider $n$-twist annulus modifications in more general
setting to show that any exotically slice knot can be obtained by the image of
the unknot in the boundary of a smooth $4$-manifold homeomorphic to ${B}^4$
after an annulus modification.
