We study classical and quantum hidden symmetries of a particle with electric charge in the background of a Dirac monopole of magnetic charge subjected to an additional central potential ( ) = ( ) + ( ) with ( ) = $$ \frac{1}{2} $$ , similar to that in the one-dimensional conformal mechanics model of de Alfaro, Fubini and Furlan (AFF). By means of a non-unitary conformal bridge transformation, we establish a relation of the quantum states and of all symmetries of the system with those of the system without harmonic trap, ( ) = 0. Introducing spin degrees of freedom via a very special spin-orbit coupling, we construct the $$ \mathfrak{sop} $$ (2 2) superconformal extension of the system with unbroken $$ \mathcal{N} $$ = 2 Poincaré supersymmetry and show that two different superconformal extensions of the one-dimensional AFF model with unbroken and spontaneously broken supersymmetry have a common origin. We also show a universal relationship between the dynamics of a Euclidean particle in an arbitrary central potential ( ) and the dynamics of a charged particle in a monopole background subjected to the potential ( ).