i used to extract fish DNA from fin tissue as well, it is more convenience without killing the organism. Do you mean polymerasation with amplification? I think PCR is robust technique to amplify, as long as you get a good quality of DNA.
Fin tissue is a good way to take DNA if you have Ethanol to store the fin in. Take a good sized chunk of one of the ends of one of the lower fins (it grows back fairly well). Otherwise, I use scales, which can be removed with tweezers and then kept in small envelopes. The scales dry and encase mucous, meaning that the DNA is preserved. I have just been extracting DNA from scales that have been kept in envelopes in a drawer for over 10 years.
Scales give less DNA, but it is easier to store and is less intrusive. There are a number of online protocols specific for extracting from scales, but I find it helps to just use twice the normal amount of Proteinase K as you would use for a normal tissue extraction.
Both of the above can be used whilst causing minimal distress for the fish (though I suggest anaesthetic for the fin clipping).
If you have a dead fish, then go for the muscle, 20mg should be enough, about the size of a fingernail clipping.
We use as well fin clipping for number warm water aquaculture like rohu, calta and silver carp and preserved the tissues in 2 ml plastic vials having ethanol. Our samples have been sent to a Australian molecular lab. for DNA analysis using the latest markers viz. SNP.