You have a wide range. At the end of Qing Dynasty, the coverage of Dengzhou Prefecture was much wider, except Laizhou City and Laixi City in Qingdao, which was basically equivalent to Weihai City and Yantai City now. It is equivalent to more than half of Jiaodong Peninsula. You should try to collect some information, such as whether your ancestral home is near the sea, mountains, rivers and ponds.
If none of these are available, you can search all the villages named after Zheng in these areas online and call them one by one for advice. Of course, these Jiazheng villages may also know some basic information about each other. You know the situation of a village, and all the villages near him know it.