  Geometrically confined superconductors often experience a breakdown in the
quantization of magnetic flux owing to the incomplete screening of the
supercurrent against the field penetration. In this study, we report that the
confinement of a magnetic field occurs regardless of the dimensionality of the
system, extending even to 1D linear potential systems. By utilizing a
vector-field magnetic force microscope, we successfully create a
vortex-antivortex pair connected by a 1D unquantized magnetic flux in
ultra-thin superconducting films. Through an investigation of the manipulation
and thermal behavior of the vortex pair, we uncover a long-range interaction
mediated by the unquantized magnetic flux. These findings suggest a universal
phenomenon of unquantized magnetic flux formation, independent of the geometry
of the system. Our results present an experimental route for probing the impact
of confinement on superconducting properties and order parameters in
unconventional superconductors characterized by extremely low dimensionality.
