@sureshp89882164 

you can use field level WRITE ACL on assigned to field. Use this in advanced script

if (current.isNewRecord())
    answer = true;
else
    answer = gs.getUser().isMemberOf(current.assignment_group) || gs.getUser().isMemberOf("Global Group name");

If my response helped please mark it correct and close the thread so that it benefits future readers.