Step 1: Energy balance
The retarding potential energy $eV_{0}$ equals the maximum kinetic energy of the emitted electrons.
Step 2: Meaning
All the kinetic energy is used up against the retarding field.
Step 3: Eliminate
The electrons are not described by zero potential energy or greater kinetic energy, and the maximum kinetic energy is what was used up. So kinetic energy $=0$.
Final Answer:
The kinetic energy of the photoelectrons is reduced to zero.
\[ \boxed{\text{(A) }\text{kinetic energy }=0} \]