  We determine generally the spinor Green's function and the twisted spinor
Green's function in an Euclidean space with a conical-type line singularity. In
particular, in the neighbourhood of the point source, we expree them as a sum
of the usual Euclidean spinor Green's functin and a regular term. In four
dimensions, we use these determinations to calculate the vacuum energy density
and the twisted one for a massless spinor field in the spacetime of a straight
cosmic string. In the Minkowski spacetime, we determine explicitly the vacuum
energy density for a massive twisted spinor field.
