  In this paper we have studied a new form of Non-Commutative (NC) phase space
with an operatorial form of noncommutativity. A point particle in this space
feels the effect of an interaction with an "{\it{internal}}" magnetic field,
that is singular at a specific position $\theta^{-1}$. By "internal" we mean
that the effective magnetic fields depends essentially on the particle
properties and modifies the symplectic structure. Here $\theta $ is the NC
parameter and induces the coupling between the particle and the "internal"
magnetic field. The magnetic moment of the particle is computed. Interaction
with an {\it{external}} physical magnetic field reveals interesting features
induced by the inherent fuzziness of the NC phase space: introduction of
non-trivial structures into the charge and mass of the particle and possibility
of the particle dynamics collapsing to a Hall type of motion. The dynamics is
studied both from Lagrangian and symplectic (Hamiltonian) points of view. The
canonical (Darboux) variables are also identified. We briefly comment, that the
model presented here, can play interesting role in the context of (recently
observed) {\it{real}} space Berry curvature in material systems.

High Energy Physics - Theory;Mesoscale and Nanoscale Physics;Quantum Physics