Yes , it is possible that an object has non-zero kinetic energy at maximum height , But how ?
Suppose you’ve thrown a body in an oblique path ( Parabolic Path ) , At maximum height , vertical component of velocity becomes zero , but horizontal component of velocity is still present there , Hence , No Doubt Kinetic Energy has been reduced at maximum height but it is still present in the less quantity , because most of the energy has been converted into the potential energy