Size of the Ground plane for designing of an Antenna

What should be the size of a Finite ground plane and Infinite ground plane in terms of wavelength for an Antenna?....

For sure it depends on the antenna. Some antennas don't require any ground plane. A rule-of-thumb for you is to use 3 to 5 wavelength for a ground plane, but the more the better always.

in some antennas ground plane is just double the size of the patch also.

u can use any size of ground plane
but depends on constraint. when you will increase ground plane size gain will increase