Perform dissociation curve, observe the temperature of the non-specific template and the specific template (higher temperature for sure) and change your program so that your detection temperature is between them. I mean, If the non-specific has 65 degrees and the specific is 72 degrees, you have to choice 68 for example for detection. Not lower than 65. If your detection temperature is lower, you are quantifying both products. If your detection temperature is between 65 and 72, you only quantify the good product.

I hope I can explain myself properly.

All the best

thanks alberto ur advice is usefull 

I got answer we were using the melt curve programme at 60 but primer tm was 62.1 so the unintended peak of residual primer was coming 

Glad to help you!