My father left my Mother and me when I was a baby. He left for work and never came back. He left her with debt a loan her dad co signed, and his two children. I have never met him and he has never contacted us or attempted to know us. He has never provided any line of support including financial support. My mother had to file for support by abandonment since she didn't even know where he was. Throughout my life I have had to deal with feelings of abandonment and financial strain but even worst, he has taunted us by calling and saying "guess who" never identifying himself among other things causing me to also grow up with a fear of this man I never met. Can I sue for the pain and psycological issues he has caused me and lack of financial support throughout my life?

You can sue anyone for anything, winning is a different matter, in short, NO as YOU do not have a cause of action.
Your mother may well have, especially when it comes to financial support.
YOU would need to prove paternity before you could even consider any action.