According to the information you provided, your father is Zezi generation, grandpa is Zhongzi generation, and you are Shuzi generation. These characters are the generation symbols of each generation in the family, which are usually stipulated by ancestors and recorded in the genealogy. Because different families have different rules for word generation, only your family members can provide more specific information.
If you have more questions, you can also consult local family culture research institutions or historians. They may be able to provide more help and information.