Modem auto detects baud rate when we press a AT command number of times.

Wrong, You don't need to send AT severnal times once is enough.

If he gets that then it means his modem baud rate is now set to 9600 and he can use it with MCU (but afterward he then should not try to get OK response at other baud rate setting)

But Automa Baud detection work some / doesn't work some time.
Best solution is to get OK response by changing PC baud rate and then using that baus rate set Modem baud rate to 9600.

Do you mean kunal has to attach his modem to PC to set the baud rate to 9600 and then detach and put it onto micro. and this has to be done every time he wants to use his modem with micro.

Regards,
Prahlad Purohit