Star Fragments in Tears of the Kingdom is a type of element that you can use for several purposes. However, it's not something you can buy or create on your own.
Star fragment drops from the Shooting Stars and can be generally found where the Shooting Star lands. These are rare and highly valuable materials that can light up their surroundings. You can find them at any time of the day, but you just have to keep looking for a shooting star and follow it to where it lands.
How To Get Star Fragments
Star Fragments are generated randomly, and there are no fixed locations from where you can find them. It's all about your luck; you might spot a shooting star in the sky if you are lucky enough. However, you can expect a shooting star once every night. Keep looking at the Sky; luckily, you might come across a shooting star flying above your head. Pay attention to them cause it's the only time you get a star fragment. However, these Star Fragments only stay for a short time and will diminish after a specific landing time if they are not collected.
A shooting star will leave a trail of light behind it from the sky, which makes it relatively easy for you to find it. Grab yourself a horse to be fast, and follow the trail to reach the landing spot of the shooting star. You will find the Star Fragment there if you reach there on time. You can also find a shooting star sometimes when skydiving or paragliding. If you are lucky enough to watch it come to the ground with you, try to get close by gliding towards it—once you are close enough, press ‘A’ to collect the star fragment mid-air.
How To Use Star Fragments
There can be several uses for the Star Fragments, starting from using it as a weapon or selling it to earn money.
Use It As A Lamp
Star fragments can act as a lamp and help Link get a light source during his nighttime adventure. This might be particularly helpful when exploring any dark place in Hyrule. Due to its illuminating properties, you can just use it as a light source in any establishment you have created. Or, if you are out in the wilds alone, fuse it with your shield, and you can carry it on your back while it lights up everything around you.
Fuse With Weapon
You can use your Fusion ability to fuse the star fragment with your weapon. Star Fragments can add extra Magic Damage once it's fused with your melee weapons. Since fusion helps to combine the weapon's properties and the material, you can shoot light beams from your weapons.
Cook It
You can also use the Star Fragments as an ingredient to cook dishes that provide you extra stats from the food you cook. Simply put the fragment in the cooking pot and the other ingredients needed for the recipe you want to create. Star Fragments can increase the buff you get depending on the recipe and what buff it provides.
Upgrade Armor From Great Fairy
Star Fragments can also be used to upgrade your armor. For that, you will have to talk with a Great Fairy. This is an easy way to upgrade armor, giving you massive advantages during combat against enemies and survival in Hyrule.
Sell It
If you are not interested in using any Star Fragment for your own, you can just trade it in a shop. You can sell each Star Fragment for 200 rupees each. This is an easy and quick way to get some rupee in Tears of the Kingdom. However, there is a better usage of the fragments for you.