Q: If a medieval society had no access to gold, what other minerals or gems could take its place in the making of coins? What other materials could replace gold coins? Jade coins? Quartz coins? Bonus points if they are easy to extract.
Short answer: ca 18x the weight in silver coins would do, to replace a gold coin
When you wanted to pay the amount of this coin you go to the coin trader..
He weighs the coin using his reference weights to be 3.3 grams, the knows this coin is a Guilder of Philippe the Beautiful of Flanders, worth 20 silver stuivers and weighing in about 3 grams each. So 3.3 grams of gold is worth 60 grams of silver, about 18x its weight. That ratio changed with colonization, where cheap South-American silver became available in Europe.
Longer answer: difficult.. gold has a perfect value/weight ratio
BUT.. suppose you'd need to buy a house in Amsterdam in 1500. The house would cost you e.g. 4600 gold-guilders, that is some 15 kg of gold, which can be carried. With the silver solution you would have to transport more than 270 kg of silver stuivers ! So gold was handy for large sums.
Thing is, "gold" is a quite flexible substance touching a sweet spot with genus Homo. We love gold. It looks nice darkish shiny yellow, it weights in hand, so you know it is really gold.. and it feels warm.. a medieval coin trader could feel the difference without even looking at the coin. This one's "no good". Gold is the standard, everything below it was counted to yield one gold coin.
Coins are coined: the new material needs to be stamped
Suppose you'd replace gold and not use silver. Your new material will be distributed in standard weight and stamped: it should be reproduced in reasonable quantities (thousands) and it will show the king's portrait, or a heraldic symbol, a text referring to the issuer, and some connecting religious symbol, like a holy text, or a cross. Don't underestimate the importance of a standard ! All German Goldguldens had the same weight and looked the same you could spend it anywhere along the river.
Jade, ivory and gemstone are about the only materials that were available in medieval times and could be engraved easily. These materials were costly imports.. maybe as expensive as gold.. but how to aquire enough of it, in large quantities, without handing over Europe to the Chinese, or the Malinese ?
There's precious objects to replace gold, but will they last for long? Do they keep value?
Funny 17th century example
You could buy a house in Amsterdam in 1639 when you sold ONE precious tulip.
A completely anonymous "coin" would be diamonds. Diamonds was the precursor of crypto-currency. You can always sell diamonds and get a price per weight unit. You'd get a very small diamond as replacement for a gold coin, I wonder if medieval coin scales were advanced enough to measure grains of diamond.
"New material easy to extract"
Glass would be a candidate.. or even paper ! No bonus for me. Yes, it would come in handy, when the new material would be less rare, or easy to obtain. That is what we do with modern, paper money. That is because we trust the banks. In medieval times, you had banks, but these were only for the rich and privileged elite, to finance their wars. In medieval times, people traveled around. You need face value money. The French introduced the first paper money, the assignates to finance the war, but in 1791, "medieval times" had long passed.