I accidently lost my downloaded files, or partially downloaded files when i hit delete by mistake!!!and I need to know if I can retrieve them in some way as if there were a history or formerly downloaded list somewhere in the Tixati program?! HELP, Please!!!

If you deleted the actual files from your hard drive (such as when using the option "Remove And Delete Local Files" on Tixati's transfers window), there is obviously no way of retrieving them through Tixati.

What you could do if that is indeed the case, is checking your operative system's possibilities of recovering deleted data - in the typical Windows system, that means checking your Recycle Bin or considering to use a Restore Point, for instance (you may want to consult your operative system's manual or inline "help" documentation, or contact their support for more detail with any of those if you need it).

Are you sure, however, that you deleted the actual files and not just the torrents from the transfer window ? If so, it would be a simple matter of re-adding the torrents to Tixati from the same place you've downloaded them, making sure to specify the same destination folders as before on your system, and use the Tixati "Local Files - Force Check" option.