Trojan virus keeps reappearing every time I scan

Every time I conduct a scan, the same trojan virus is identified and quarantined on my MAC computer.  I consulted the tech staff at Norton twice.  The first time, the technician deleted the virus, but the next time I booted  my computer, the Norton Program would not load.  The second technician uninstalled and reinstalled the program which worked until I rebooted my computer.  I next consulted a technician from my local university.  He uninstalled and reinstalled the program but when reinstalling it, it did so as if he were installing it on a new machine (one of the selections).  This solved the problem for about a week.  Unfortunately, the problem reappeared and is now chronic every time I shut down and restart my computer and conduct a scan.

Any suggestions?