How can i compare the time stamps of two files to check if they are the same. Is there any option like the -nt or -ot with the if clause? I have a file and i "cp -p" the file to a different location. If a copy of the file already exists, i dont want to copy it. I am also running multiple instances of the script that copies the file and i do not know the exact name of the file that gets copied because the script appends timestamp to filename at the time of copying.

If you have timestamps in the names, just compare the names. But you can do:
[[ $filea -nt $fileb || $filea -ot $fileb ]] && echo files have different mod times