This is a list of exoplanet discoveries that were the first by several criteria, including:
and others.
The choice of "first" depends on definition and confirmation, as below. The three systems detected prior to 1994 each have a drawback, with Gamma Cephei Ab being unconfirmed until 2002; while the PSR B1257+12 planets orbit a pulsar. This leaves 51 Pegasi b (discovered and confirmed 1995) as the first confirmed exoplanet around a non-compact star.
Some of these planets had already been discovered by another method but were the first to be detected by the listed method.