I gave a list of all known genuine coinage in the name of Edward VIII in
this old thread. As mentioned above, apart from the trial British threepences, none of them have the king's portrait on them.
There is a tradition on British coinage that a new monarch is supposed to face in the opposite direction to their predecessor; Edward's father George V faced left, so Edward VIII was "supposed to" face right. The story goes that the king was displeased with this tradition, because it would've meant nobody would see the part in his hair.
"Coins" like this one fill a perceived demand from collectors, who would like to have a "coin" with a portrait of each British monarch. As "coin-like objects", they're listed in the "Unusual World Coins" catalogue.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis