The idea of fermion mass generation through Yukawa couplings between Higgs
bosons and fermions may be tested by their associated production at future
linear colliders (LC). We study the production mechanism in the minimal sup
ersymmetric standard model at photon colliders that can be realized by the
laser back-scattering technique at a LC. We find that the cross sections fo
r the production of the light Higgs-boson-top-quark pair, heavy-Higgs-boson
-bottom pair and pseudoscalar Higgs-boson-bottom pair can reach the level o
f similar to 1.0 fb or higher for phenomenologically favored values of the
parameters in the Higgs sector. Since this mechanism is not affected by the
appearance of Higgs resonances as in electron collisions, it may provide a
more sensitive way to determine the Yukawa couplings between Higgs bosons
and heavy quarks.