A method for making an enriched population of polynucleotides comprising target sequences from biological samples, each sample characterized by a genome, the method comprising: (a) A-tailing duplex polynucleotide fragments from the genomes of the biological samples to produce A-tailed polynucleotide fragments; (b) ligating a first adaptor to the A-tailed polynucleotide fragments from each sample to produce ligated polynucleotide fragments, wherein each sample is in a separate reaction mix, and wherein the first adaptor comprises: a 5' top strand that comprises from 5' to 3': a leader sequence, a sample tag unique to each separate reaction mix, and a sequence that is complementary to a 3' bottom strand; the 3' bottom strand comprising at least one modified nucleotide and not the sample tag nor the leader sequence, wherein at least some of the polynucleotide fragments in each sample comprise a target sequence; (c) pooling the ligated polynucleotide fragments into a single reaction mix to form pooled polynucleotide fragments; (d) hybridizing an oligonucleotide having an affinity binding domain to the 3' end of the target sequence on each strand of the pooled polynucleotide fragments to form duplexes, each duplex comprising one of the pooled polynucleotide fragments, and immobilizing the duplexes on a substrate to form immobilized duplexes; (e) removing from the immobilized duplexes any 3' non-target single stranded overhang sequences to form a polynucleotide-oligonucleotide duplex having a double-stranded end; (f) ligating a second adaptor, optionally having an index sequence, to the double-stranded end of the polynucleotide-oligonucleotide duplexes to form second adapter ligation products, wherein: (i) the second adaptor has a duplex at its 5' end and a 3' single strand overhang with a terminal 3' -5' exonuclease blocking moiety on its 3' end; and (ii) the duplex 5' end has a top strand and a bottom strand where the bottom strand has at least one modified nucleotide; (g) enzymatically degrading the modified nucleotides of the second adaptor ligation products to form a single stranded polynucleotide immobilized on a substrate by the hybridized oligonucleotide; and (h) removing immobilized polynucleotides that do not contain target sequences using a 3'-5' double-stranded exonuclease to form the enriched population of single stranded polynucleotides comprising target sequences. (a) A-tailing duplex polynucleotide fragments from the genomes of the biological samples to produce A-tailed polynucleotide fragments; (b) ligating a first adaptor to the A-tailed polynucleotide fragments from each sample to produce ligated polynucleotide fragments, wherein each sample is in a separate reaction mix, and wherein the first adaptor comprises: a 5' top strand that comprises from 5' to 3': a leader sequence, a sample tag unique to each separate reaction mix, and a sequence that is complementary to a 3' bottom strand; the 3' bottom strand comprising at least one modified nucleotide and not the sample tag nor the leader sequence, wherein at least some of the polynucleotide fragments in each sample comprise a target sequence; a 5' top strand that comprises from 5' to 3': a leader sequence, a sample tag unique to each separate reaction mix, and a sequence that is complementary to a 3' bottom strand; the 3' bottom strand comprising at least one modified nucleotide and not the sample tag nor the leader sequence, wherein at least some of the polynucleotide fragments in each sample comprise a target sequence; (c) pooling the ligated polynucleotide fragments into a single reaction mix to form pooled polynucleotide fragments; (d) hybridizing an oligonucleotide having an affinity binding domain to the 3' end of the target sequence on each strand of the pooled polynucleotide fragments to form duplexes, each duplex comprising one of the pooled polynucleotide fragments, and immobilizing the duplexes on a substrate to form immobilized duplexes; (e) removing from the immobilized duplexes any 3' non-target single stranded overhang sequences to form a polynucleotide-oligonucleotide duplex having a double-stranded end; (f) ligating a second adaptor, optionally having an index sequence, to the double-stranded end of the polynucleotide-oligonucleotide duplexes to form second adapter ligation products, wherein: (i) the second adaptor has a duplex at its 5' end and a 3' single strand overhang with a terminal 3' -5' exonuclease blocking moiety on its 3' end; and (ii) the duplex 5' end has a top strand and a bottom strand where the bottom strand has at least one modified nucleotide; (i) the second adaptor has a duplex at its 5' end and a 3' single strand overhang with a terminal 3' -5' exonuclease blocking moiety on its 3' end; and (ii) the duplex 5' end has a top strand and a bottom strand where the bottom strand has at least one modified nucleotide; (g) enzymatically degrading the modified nucleotides of the second adaptor ligation products to form a single stranded polynucleotide immobilized on a substrate by the hybridized oligonucleotide; and (h) removing immobilized polynucleotides that do not contain target sequences using a 3'-5' double-stranded exonuclease to form the enriched population of single stranded polynucleotides comprising target sequences.