I have attached a protocol have used before to extract genomic DNA from ticks. it gives good quality DNA. For a specific gene, you need to design primers from the flanking region of the gene, which could be conserved across species. Which gene are you targeting? Included in the attached document is a PCR protocol for amplification of cytochrome c oxidase gene which is relatively conserved in a range of genera of ticks, so the primers are almost universal.
To extract DNA from ticks or mites, you have to go for one of the known protocols and you can find them on the internet or if you can use one of those commercially available kits from the market..
If u have any other question, please feel free to ask.