:salam2:
As far as my little knowledge goes, you can not build a mosque with only one fund from one particular person. Others will have to chip in and it has to be a collective effort to build a mosque. There is nothing like a private mosque. You can have your private prayer room at your home/work, etc. But not a private mosque. Mosques are places to prostrate before Allah, for everyone. So you can not have your own private mosque. But you can make a collective effort along with others to build a mosque, as that will be your source of income for good deeds even after you die.
Allah knows best.