  We find all $P$-resolutions of quotient surface singularities (especially,
tetrahedral, octahedral, and icosahedral singularities) together with their
dual graphs, which reproduces Jan Steven's list [Manuscripta Math. 1993] of the
numbers of $P$-resolutions of each singularities. We then compute the
dimensions and Milnor numbers of the corresponding irreducible components of
the reduced base spaces of versal deformations of each singularities.
Furthermore we realize Milnor fibers as complements of certain divisors
(depending only on the singularities) in rational surfaces via the minimal
model program for 3-folds. Then we compare Milnor fibers with minimal
symplectic fillings, where the latter are classified by Bhupal and Ono [Nagoya
Math. J. 2012]. As an application, we show that there are 6 pairs of entries in
the list of Bhupal and Ono [Nagoya Math. J. 2012] such that two entries in each
pairs represent diffeomorphic minimal symplectic fillings.
