Would it be possible to detect a magnetic field around an exoplanet? Of course, we can't fly a magnetometer next to an exoplanet to measure the magnetic field, but might it be possible to find indirect evidence (e.g. polar auroras) of a magnetic field generated by an exoplanet? Has this already been done?
You usually look for electronic synchrotron emission in the radio, which corresponds to the magnetic field strength expected for giant planets. There has been a single detection claimed with LOFAR by Turner et al., (2020) around $\tau$ Bootes, but it's very noisy and hence disputed.
Other effects like Zeeman-splitting have been considered for detection, but require clean, high-resolution signals from planets. So far this is too difficult to perform due to stellar contamination.
Magnetic field searches around brown dwarves have been more successful, but those are not planets, of course.