microstrip lines with ground plane slots

Microstrip lines with periodic ground plane slots has characteristics of a bandstop filter. The stopband frequency can be chosen depending on the dimensions and distance between the periodic slots.

Is there any way that we can control the bandwidth and its attenuation at the stopband frequency?

try changing the impedance of the lines between the slots on the top side. The 1st and last line will be the same impedance, the 2nd and 2nd to last line will be another impedance, etc. By varying the impedance of the lines, you should be able to control the "coupling" into the stopband structure, changing the bandwidth.