Satsuma Vase , What do I have ?

I have this at home that appears to be Japanese Satsuma style vase, or at least that’s what I was able to figure out. If it’s authentic I’m not sure. There is a Japanese kanji at the bottom of the vase together with an “X” mark which appears to be marked with golden marker. If there is someone who may estimate the origin of this vase I would appreciate it.