  In this work we consider fermionic zero modes in the external scalar and
electromagnetic field forming the vortex on a sphere. We find the
correspondence between the equations for the fermions in different dimensions,
find their explicit expressions through the vortex fields in case of massless
fermions, asymptotics near the poles in case of massive fermions and check the
number of the solutions by proving index theorem for the fermions on a sphere.
As a part of deriving the index, we write a detailed calculation of the Green
function of the Heat equation.
