You can use an -exec directive of the command cleartool find in order to chain a grep command:
# Windows syntax 
cleartool find . -type f -branch 'brtype(MyBranch)' -exec "grep aSpecificString \"%CLEARCASE_PN%\""
# Unix syntax
cleartool find . -type f -branch 'brtype(MyBranch)' -exec 'grep aSpecificString "$CLEARCASE_PN"'
Note the -type f, to limit the search to files (not directories).
Note also that you will get the same file multiple times, if there are several versions of that file in the branch MyBranch.
To limit to one file result per branch, replace -branch by -ele (for 'element')
(as I illustrated in "How to find the files modified under a clearcase branch"):
# Unix syntax
cleartool find . -type f -ele 'brtype(MyBranch)' -exec 'grep aSpecificString "$CLEARCASE_PN"'