The Johannsen-Psaltis spacetime describes a rotating black hole with parametric deviations from the Kerr metric. By construction this spacetime explicitly violates the no-hair theorems. Rotating black hole solutions in any modified theory of gravity could be written in terms of the Johannsen-Psaltis metric. We examined the accretion of gas onto a black hole described by the static limit of this spacetime. We employed a potential that generalises the Paczynski-Wiita potential to the static Johannsen-Psaltis metric. Our analysis utilised a recent pseudo-Newtonian formulation of the dynamics around arbitrary static, spherically symmetric spacetimes. We found that positive (negative) values of the scalar hair parameter, $\epsilon_{3}$ increased (decreased) the accretion rate. This framework can be extended to incorporate various astrophysical phenomena like radiative processes, viscous dissipation and magnetic fields.