  We propose an exactly solvable model of one-dimensional anyons with competing
$\delta$-function and derivative $\delta$-function interaction potentials. The
Bethe ansatz equations are derived in terms of the $N$-particle sector for the
quantum anyonic field model of the generalized derivative nonlinear
Schr\"{o}dinger equation. This more general anyon model exhibits richer physics
than that of the recently studied one-dimensional model of $\delta$-function
interacting anyons. We show that the anyonic signature is inextricably related
to the velocities of the colliding particles and the pairwise dynamical
interaction between particles.
