  A major issue for the implementation of large scale superconducting quantum
circuits is the interaction with interfacial two-level system defects (TLS)
that leads to qubit relaxation and impedes qubit operation in certain frequency
ranges that also drift in time. Another major challenge comes from
non-equilibrium quasiparticles (QPs) that result in qubit dephasing and
relaxation. In this work we show that such QPs can also serve as a source of
TLS. Using spectral and temporal mapping of TLS-induced fluctuations in
frequency tunable resonators, we identify a subset of the general TLS
population that are highly coherent TLS with a low reconfiguration temperature
$\sim$ 300 mK, and a non-uniform density of states. These properties can be
understood if these TLS are formed by QPs trapped in shallow subgap states
formed by spatial fluctutations of the superconducting order parameter
$\Delta$. Magnetic field measurements of one such TLS reveals a link to
superconductivity. Our results imply that trapped QPs can induce qubit
relaxation.
