A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force 'F' is applied at height 'h' from the lowest point. For the maximum acceleration of centre of mass, which is correct : -

The surface is smooth, so there is no friction. The only horizontal external force on the sphere is F.
By Newton's second law for the centre of mass: $a_{cm} = \dfrac{F_{ext}}{M} = \dfrac{F}{M}$
This does not depend on where the force is applied. The height h only changes the torque about the centre, i.e. how much the sphere spins, not the acceleration of its centre of mass.
Since the surface is smooth, rolling without slipping is not possible; the sphere simply moves linearly (with some rotation if $h \neq R$).
So there is no relation between h and R for the maximum acceleration of the centre of mass; it is always $\dfrac{F}{M}$.