Killing spinor equations are equations that result from supersymmetric transformations. One example of those is for example is in $N=2$ Supergravity theories.
As suggested by some books and papers on the web, there is the vanishing of the gravitini supersymmetry.
So if fermions here should vanish in $N=2$ supergravity theories, what KSE's should we see in $N=2$ sugra?
Answer
If we want to find a background preserving some supersymmetry then by assuming that fermions vanish, we have to find a combination of the bosonic fields such that the supersymmetry variation of the fermionic fields is zero. It means that all supersymmetry variations of fermions are required to vanish, not only gaugino or gravitino.
I am not very familiar with $N=2,D=4$ SUGRA, but it seems like in this case the variations are the first, third and forth line in eq (9.46) http://itf.fys.kuleuven.be/~toine/LectParis.pdf They are respectively the variations of gravitino, gaugino and hyperino.
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