As David mentioned, designing new primers would be the simplest option. There are a couple of factors to consider. First, what are the length of the primers you have designed that overlap with the mutation site? Second, do you know where the mutation is along the amplicon? Is it a single base mutation, an indel or a mutation of multiple bases? Do you know what the flanking sequences are to the amplicon? This would allow you to select primers outside the amplicon to generate a larger product and avoid the mutation site.
There are a couple of possible things you could try. If you know where the mutation site is, you could design primers used specifically to amplify the product with the mutation. For example if the mutation has a C instead of an A on base 18 of the forward primer. Then design both primers separately and amplify the product with each one to see which produces the better amplification. In theory, the primer with the correct match to the mutation should amplify better than a primer containing a mismatch. Another option is to design a somewhat shorter primer that will not overlap the mutation site and tail with additional bases on the 5’ end. During amplification, the tailed primer should add additional bases on the PCR product. We often added a universal primer sequence as a tail on PCR primers so we can sequence with the universal primers. This method was once associated with dye primer chemistry for detection of SNPs.
I think that if you cant move with primers to avoid overlap with the mutation site then u can go for hybridization capture sequencing. U can use fragment amplified with any of the primer pair designed to amplify from the area of ur interest and use that amplicon to capture a fragment from ur DNA pool
alternatively, trimming a primer on one side would not cause any problem
Thank you for all your answers. I have redesigned the primer sets as suggested. I found out that along a sequence only certain site can the primer binds to. I now have 3 sets of candidate primers which only varies a few nucleotides from each other binding site but the self complementarity is quite different. Is it possible to use forward primer from one set of primer then use reverse primer from the other set because I want to choose primer with low self complementarity? The product length is only 2~3 nucleotide difference.