  We study the combined effect of world-volume and background fluxes on
Euclidean D3-brane instantons in F-theory compactifications. We derive an
appropriate form of the fermionic effective action, in which the fermions are
topologically twisted and the dynamical effect of fluxes, non-trivial
axio-dilaton and warping is taken into account. We study the structure of
fermionic zero modes, which determines the form of possible non-perturbative
superpotential and F-terms in the four-dimensional effective action. Invariance
under SL(2,Z) is discussed in detail, which allows for an interpretation of the
results in terms of the dual M5-brane instanton in the M-theory picture. We
also provide the perturbative IIB description in the orientifold limit, when
available. Furthermore, we consider the possible inclusion of supersymmetry
breaking bulk fluxes and discuss its implications.
