  We have studied the distinctive features of the
Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) instability and phase transitions in
two--dimensional (2D) mesoscopic superconductors placed in magnetic field of
arbitrary orientation and rotating superfluid Fermi gases with imbalanced state
populations. Using a generalized version of the phenomenological
Ginzburg-Landau theory we have shown that the FFLO states are strongly modified
by the effect of the trapping potential confining the condensate. The
phenomenon of the inhomogeneous state formation is determined by the interplay
of three length scales: (i) length scale of the FFLO instability; (ii) 2D
system size; (iii) length scale associated with the orbital effect caused
either by the Fermi condensate rotation or magnetic field component applied
perpendicular to the superconducting disc. We have studied this interplay and
resulting quantum oscillation effects in both superconducting and superfluid
finite -- size systems with FFLO instability and described the hallmarks of the
FFLO phenomenon in a restricted geometry. The finite size of the system is
shown to affect strongly the conditions of the observability of switching
between the states with different vorticities.
