Why is this a fake coin, just because it's not in Remmelts does not mean it is fake. There are more cash coins not mentioned in Remmelts than there are. Remmelts in fact is a small reprint of the Schjöth catalog. The pictures are drawn and do not always very reliable.
This coin was issued by The Prince of Lu about 1644-1646 (He was one of the 4 princes of the Southern Ming) The characters mean Da Ming Tong Bao (top, bottom, right, left), and is actually on of the hardest to find. It is worth about 50 USD and infact the only type I'm missing of this period. Da Ming therefore is the name of the Ming Dynasty.
The picture was taken from Cast Chinese Coins by David Hartill