Gold is one of the densest metals in existence. Only few metals and alloys are heavier, but they are not much easier to obtain, like iridium, osmium, neptunium and plutonium (!).
If you use any lighter metal and try to make it look like gold you will be discovered and beheaded - the method of finding out density of alloys pretending to be gold was discovered by Archimedes around 200BC: https://en.wikipedia.org/wiki/Eureka_(word)

Luckily for you, contrary to common myth the alchemists were not tasked with transmuting common metals to gold. At least not by smart princes. If you think about it - why would a magician who can produce gold out of common elements even need an employer? to take all the gold from him? That's the opposite of what most smart people look for in employment :)

Alchemists, at least those in princely courts, were very educated people. They were doing something much more useful than transmutation - they were improving quality gun alloys and of gunpowder. We're talking about an era when artillery becomes common and important element of battlefields, and handguns are improving to be actually somewhat useful too.

The stories of alchemists dealings with Satan are rumours originating in the smell of sulfur and mysterious fires coming from their workshops as misunderstood by the less educated courtiers. Also probably used as useful cover stories by princes who wanted their real interests secret from their cousins in other courts.

In conclusion: don't bother with gold. Learn how to make really good gunpowder and maybe some alloys, and the prince will give you gold instead of waiting for you to make it from dirt.

Your modern chemist would be foolish to even try to make or fake gold. Instead, you make something that will cause other people to willingly give you THEIR gold. For instance, look the commercial possibilities in the aniline dyes, which should be easy for a modern chemist, and from which fortunes were made in our own history: https://library.si.edu/exhibition/color-in-a-new-light/making

The only answer is platinum

Many other answers have pointed out the density problem. Since Archimedes was able to determine the difference between pure gold and electrum (gold alloyed with silver) using density, this should be a reasonably well known process for an 'expert' king. If you really want to trick the king into thinking he has gold, the only element that has most of gold's physical attributes (malleable, ductile, non-reactive, and very very dense) is platinum.

However, there is still one significant difference: melting point. Pure platinum would not be meltable with 1500s technology, you can't get a fire hot enough until the coke ovens of the later Industrial Revolution. A wise proto-chemist will know this isn't exactly gold. But, I'd hardly say that is disqualifying. If gold is valuable, how valuable is unmeltable gold (you can call it aurum indissolubilis in Latin)?

How to get some platinum

There are two basic ways you can separate platinum.

First, from nickel based ores, you can try to separate it magnetically. Platinum is paramagnetic, unlike ferro-magnetic nickel and iron. If you run an electromagnet over ground up ore, you could separate out the platinum. This won't be cheap or easy, but with some obedient apprentices, some copper wire, and a watermill, you could build both an ore grinder and a basic dynamo.

Second, you can electro-refine a copper ore. You basically make unrefined copper ore into a battery in a sulfuric acid bath (sulfuric acid was known as 'oil of vitriol' at the time, so you could get your hands on it). The majority copper will be dissolved into the acid bath, while the less reactive (or 'noble') elements like gold, silver, and platinum will end up in the sludge at the bottom.

So the real challenge is then finding ore with platinum in it. There, I can't really help you, I'm not sure how to identify those ores. But, hopefully, the chemist going back in time has some time to prepare, and get some mining maps or something.

Conclusion

If the goal is to simulate creating gold, the best way to do it is to separate platinum from various ores, using one of the two listed methods. This is about as close as you will get to the Philosopher's stone without a nuclear reactor to help you out.

Forget gold. You can't do it. You can't even come close. If your prince wants riches, how about synthetic gemstones?

You might be able to produce diamonds through the chemical vapor deposition process, but the stones produced will be tiny, and prior to De Beers' marketing push, they were considered a fairly boring gemstone.

You could put together a suitable oxyhydrogen torch, and fuse alumina into synthetic rubies and sapphires. Alumina is pretty ubiquitous, and you can vary the color by adding trace amounts of iron, copper, chromium, and other metals to the mix.

Synthetic emeralds are probably not an option, since the techniques for making them are still mostly trade secrets, and appear to involve materials or material purities that would be unavailable in the 1500s.

The last of the cardinal gemstones, amethyst, requires high-pressure conditions for synthesis, though the main ingredient, silica, is even more common than alumina. You could try making it, but the metallurgy of the time means you're more likely to blow up your lab than produce gemstones.

Gold is nice and shiny, but you can not eat it and it does not give you any power to protect the gold you do have. But troops are nice. There are only a few problems with them.

They need feeding. So increasing food production by inventing synthetic fertilization is Huge. You need less people to grow food, you need less land for the same army production.

Another problem is logistic of army march. So you invent some basic food preservatives. Any of the simple ones will do. And you can transport much more food on longer routes. So no war of attrition against your lord.

And as for the troops equipment, steel is nice but tricky to produce.... if you don't have the right knowledge. And good steel can make your small army strong as a big one.

Conclusion

So going for something petty like producing few grams of gold-like substance is not as useful as providing your lord with the means to rob all his neighbors of the real stuff.

Afterthought

If still in a pickle, just destille some fungi juice and make him really happy

Or if you really want something with only value, then produce something like a purple dye that was in the time much more valuable then gold.

Most of the great questions of alchemy, like transmuting lead into gold and elixirs of eternal life, have not only failed to materialize but turned out to be impossible in any practical sense. So I don't think you have much potential there. As you remark, one could make counterfeit gold, but why bother when there are other much more valuable legitimate things you can make?

• Many dyes were extremely valuable, because they could only be produced through laborious processes in tiny amounts. This is why royalty wore purple, for example, it used to be very hard to make the dye and only kings could afford it.


• Aluminum used to be more valuable than gold. Many other metals were expensive because efficient production methods did not exist.


• Better steels and other alloys can be used for making very high quality weapons.


• Chemical fertilizers could greatly improve agriculture, which had a huge influence on the economy back then.


• Various methods of preserving food could provide enormous strategic advantage in war and trade.


• Electricity could be discovered centuries early. Chemical batteries are not hard to make, even modern generators are pretty straightforward if you have access to a King's craftsmen.


• Gunpowder and other explosives are very useful for military purposes, mining and construction.

Brew poisonous chemicals & create bombs etc.

A prince may be interested in Gold, in order to gain money and power.
But why ? He wants to win against his enemies: other kingdoms.

Also, the more Gold floods the market, the cheaper it becomes.

So, propose him some poisonous stuff.
It helps him to reach his goals, allowing him to easily assassinate leaders causing chaos in the other kingdoms.

Also, many poisons are easy to create and show great effect. And even more of them could be of great use in battles ! Think of grenades and other explosives, or even guns.

To make sure your chemist isn't killed, make him keep all the formulas secret, stored only in his head. That way, if the prince kills him, he looses his advantages in combat and against other kingdoms.

PS : One example for a family that made their way to power using poison would be the Borgias.

Also, think of some other nice modern chemicals you could present him : sleeping gas(chloroform) etc.

Totally different attempt : cook some meth/other drugs. Make the prince addicted. And then he'll neeever let you be killed. He'll protect you to the end of his life.

TL;DR

Forget the Gold.
Basically, with modern knowledge and basic education, you could easily become his new leading scientiest and thus hardly replaceable.
By keeping some key formulas etc. secret you can also make sure that you'll always be needed.

Also, I can think of tons of extremely useful chemicals for all purposes. Others already mentioned fertilizers.

Gold is thought to have been produced in supernova nucleosynthesis,
and from the collision of neutron stars,[47] and to have been present
in the dust from which the Solar System formed.[

Wikipedia https://en.wikipedia.org/wiki/Gold#Origins

The reason they think that is the maths show that all the gold on earth couldn't have been produced in the previous two generations of supernova the earth and sun was made from.

Making Gold cannot be done with chemistry. It requires fusion and I suspect it is endothermic. Iron is the last exothermic fusion in a sun.

As a rough rule of thumb, atomic is two magnitudes of order stronger than chemistry, and sub atomic two orders again.

Think common chemicals that have been around for a while. Like gunpowder. One big invention (that saved a lot of towns) was to make it while wet. Dry it. Smash it up with wooden hammers then sieve it. This gave quality control over grain size and thus predictable burning. And the neighbours didn't have to die.

when faced with the issue of making gold why not respond with "but your majesty certainly that would not be considered wandering into the realms of magic?" in those superstitious times were magic was feared just the mention of gold and magic should be enough to put the prince off. if this does not deter him recommend that he seeks out a witch, as magic is not something a meagre alchemist could ever perform. both situations ensure your survival and the upkeep of your reputation. instead offer him other valuable metals like steel for weapons which is certainly something that would catch his interest. tell him that it would make weapons and armour far superior to all other major powers in the world. this would be more than enough to avert his focus from gold if the previous plan fails. also if you were able to find some common medicinal plants or fungi some basic medicines could be created which would make you very popular with the army.

Other people who were asked to turn lead into gold did instead turn clay into china. Well, at least one did. If you can figure out how to create china you will make your prince very happy.