How to program a fake stm32f103c6?
Possibly, you have loaded a program that uses the SWD pins for other purposes than connecting a debugger or that otherwise negatively affects the SWD pins.

Set the BOOT0 jumper to 1 and restart the BluePill. That way, it starts in bootloader mode instead of starting your program. That way, you should be able to connect the STLink again and uplad a new program. After the upload, set the jumper back to 0.

Update

BTW. A BluePill usually has a STM32F103C8 chip (or clone), not a STM32F103C6. The difference is 64K vs 32K of flash. Make sure you have selected to correct chip.