atm security terminal using Fingerprint sensor. Help needed with the code

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3 
// pin #2 is IN from sensor (GREEN wire)
// pin #3 is OUT from arduino  (WHITE wire)
SoftwareSerial mySerial(10, 11);

Can you post a picture of the mySerial that is connected? There is NOTHING useful in that name. It's like getting a dog and calling it myDog.

SoftwareSerial mySerial2(12, 13);

Can you post a picture of the mySerial2 that is connected?

Did you read the documentation for SoftwareSerial? How many instances can listen at the same time?

   mySerial2.println("AT+CMGF=1");    //Sets the GSM Module in Text Mode
    delay(1000);  // Delay of 1000 milli seconds or 1 second
    mySerial2.println("AT+CMGS=\"+919886924719\"\r"); // Replace x with mobile number
    delay(1000);
    mySerial2.println(randNumber);// The SMS text you want to send
    delay(100);
    mySerial2.println((char)26);// ASCII code of CTRL+Z
    delay(1000);

This is like posting on the forum and never reading the replies. I don't know why I'm bothering to type one up. You won't read it.

The hardware MAY be telling you something, if only you'd listen.

It doesn't do much good to send data to the (uselessly named) mySerial2 instance since you have not called mySerial2.begin().