  Quantum sensors based on cold atoms are being developed which produce
measurements of unprecedented accuracy. Due to shifts in atomic energy levels,
quantum sensors often have stringent requirements on their internal magnetic
field environment. Typically, background magnetic fields are attenuated using
high permeability magnetic shielding, with the cancelling of residual and
introduction of quantisation fields implemented with coils inside the shield.
The high permeability shield, however, distorts all magnetic fields, including
those generated inside the sensor. Here, we demonstrate a solution by designing
multiple coils overlaid on a 3D-printed former to generate three uniform and
three constant linear gradient magnetic fields inside the capped cylindrical
magnetic shield of a cold atom interferometer. The fields are characterised
in-situ and match their desired forms to high accuracy. For example, the
uniform transverse field, $B_x$, deviates by less than $0.2$% over more than
$40$% of the length of the shield. We also map the field directly using the
cold atoms and investigate the potential of the coil system to reduce bias from
the quadratic Zeeman effect. This coil design technology enables targeted field
compensation over large spatial volumes and has the potential to reduce
systematic shifts and noise in numerous cold atom systems.
