Abstract: Methods, compositions and systems to amplify short DNA fragments, such as cfDNA, and to reduce random base errors formed in template-dependent primer extension reactions, and to find variant frequencies of mutations on the DNA fragments. The methods, compositions and systems described herein may include, or include the use of, poly(dA) tailing of short DNA fragments by a terminal deoxynucleotidyl transferase, linearly amplification and a multiplex primer extension reaction.