what is the necessary condition on a force the result the conservation of angular momentum for a particle affected by that force?

The force must be applied on the axis of rotation

Explanation:

A rotating system conserves its angular momentum only if there are no external torques on the system. In other words, the external torque must be equal to zero.

T=0

T=Fxd

Torque is equal to the vector product of a force by the distance between the axis of rotation and where the force is applied.

For this product to be zero, the force must be applied on the axis of rotation (d=0).