I don't have the schematic in my head right now. I did this job years ago. I used a UC3842 and a MOSFET.
I don't have time right now but it is common to use a UC3824 type part (or similar) and supply it power from 350V without burning much power. Read on "power-up supply" for the UC3842. I will try to get back in a while.

What is the output current?

it is about 20 mamps.

 

10 to 350 dc voltage input. I opened it and i found a simple buck converter that can do this job and it provides a 5 volt output

10V to 5V is better. 12 to 12V is hard.
Please send a picture of the 10 to 350Vdc buck converter. Maybe we can make the same thing.
How accurate must the 12V be? I think you will use the 12V to make 5V so the 12V can be a little crude.

it is about 20 mamps.

Good news.

 

10V to 5V is better. 12 to 12V is hard.
Please send a picture of the 10 to 350Vdc buck converter. Maybe we can make the same thing.
How accurate must the 12V be? I think you will use the 12V to make 5V so the 12V can be a little crude.

Good news.

 

Here is a 48 - 400V to 15V 300mA example.
It works down to 8V in other versions.
I have not used it.

It appears, if the output voltage was 5V then the min input voltage might be 16V. Maybe if the current was much less the min input voltage could be lower.