Actually, once a computer has become infected, it is too late to make a safe backup since backups should be made only from uninfected computers (such as after running antivirus and other antimalware scans). Backups taken from an infected computer will probably also be infected and can also infect another computer.
The only safe thing to do at this point is to try to clean out the infection by using a good antivirus program and various other antimalware programs, such as MBAM (sadly, I can't recommend the latest version of MBAM right now), and pray you do not lose any data in the process. If your data is critical, it would be best to turn it over to a paid data recovery professional to hopefully clean it with minimal data loss; however, that will be expensive. In fact, I strongly recommend seeking out a professional data recovery specialist. Data recovery techniques will vary with equipment and the nature of the problem so any attempt to fix it yourself will likely result in disaster since there is no way for any of us to diagnose the exact nature of your problem remotely (although there will be many people attempting to advise you on how to fix it yourself).
In the future, you need to frequently backup your computer and keep several versions of the backups so, should your latest backup(s) turn out to also be infected, you can revert to a still earlier version that was made before the computer became infected. Also, automated backups are an extremely bad idea because they would require a backup drive to be permanently connected to the computer, exposing the backup drive to the very same infection you are trying to avoid. The only way to have reasonably safe backups is to connect the backup to the computer only while updating the backup and to not update backups until you have run thorough scans with an antivirus program and with other antimalware programs.