This is an interesting task to do and thankfully you don’t need an electrical engineering degree in order to figure out how to do it. The best way to figure it out is to disassemble a Chinese made flashlight and you can see that they use just capacitors to bring down the voltage instead of a transformer. They use it to charge a small lead-acid battery. The question now is how a capacitor alone can be used to bring down 220volt down to 6 or 12 volt? What is capacitive power supply anyway?
A capacitive power supply is a type of power supply that uses the capacitive reaction of a capacitor to reduce the mains voltage to a lower voltage. There are two important limitations. First the high withstanding voltage required of the capacitor, along with the high-capacitance required for a given output current, mean that this type of supply is generally used only in low-power applications. Generally, a capacitor of a given size or budget can have a high voltage rating or high capacitance but not both. The second is that due to the absence of electrical isolation, the circuit must be encapsulated and isolated to avoid direct galvanic contact with the users.
This process is extremely unsafe. There are achievable but un economical methods to do so. You can use a capacitor divider. Replace the resistors of a resistor divider with capacitor. It is a possible way to reduce voltage. However there are two challenges. Unregulated voltage. A regulator must be used. You will need capacitors that will let pass 3 amps.
Another way to convert AC to DC without a transformer is to use electrostatic induction (capacitive dual of a transformer). It is still immature technology but possible to be modified to your application. You can use electronic circuits but they won’t be able to provide a 3A output. It won’t be more than .5A output. Why is India using 220 volts when the United States is using 110 volts of power?
You need to know your supply types and the pros and cons for each use of the product. A Capacitive supply type is a higher cost than resistive. However it is more efficient than resistive. The zero crossing is delayed. A Resistive supply type is the lowest cost but also the least efficient. The zero crossing is not delayed. The Bridge supply type is the highest cost but also the highest current capacity and efficiency. The output voltage isn’t referenced to line or neutral so TRIAC control isn’t possible.
They are using lots of transformer less power supplies in China in their small appliance products. Because transformers are big and heavy use a capacitor replace which is smaller and lighter than a transformer as a power supply. The problem is that if you touch the circuits you might get a electric shock. So, as I said before, it is unsafe. The use of transformer less power supply dates back to about 15-20 years ago.