FastQC has a list of "contaminants" that it matches against when looking for over represented sequences in your sequencing file.
The sequences listed there are parts (or all) of many of the sequencing adapters used in different library preps. I'll paste that in for you below ... you'll see there are some from an Illumina "Small Rna" prep, so perhaps those are the ones you are looking for, but if this is your data, your best bet is to obviously talk to the person who is making the libraries. If you are using data from a publication, they should cite what prep they used (or describe their own in their supplemental methods) where you can likely get the information you are after.
Also -- I'd bet you should be looking at the 3' ends of the reads to locate and strip your adapters from.
Illumina Single End Adapter 1 ACACTCTTTCCCTACACGACGCTGTTCCATCT
Illumina Single End Adapter 2 CAAGCAGAAGACGGCATACGAGCTCTTCCGATCT
Illumina Single End PCR Primer 1 AATGATACGGCGACCACCGAGATCTACACTCTTTCCCTACACGACGCTCTTCCGATCT
Illumina Single End PCR Primer 2 CAAGCAGAAGACGGCATACGAGCTCTTCCGATCT
Illumina Single End Sequencing Primer ACACTCTTTCCCTACACGACGCTCTTCCGATCT
Illumina Paired End Adapter 1 ACACTCTTTCCCTACACGACGCTCTTCCGATCT
Illumina Paired End Adapter 2 CTCGGCATTCCTGCTGAACCGCTCTTCCGATCT
Illumina Paried End PCR Primer 1 AATGATACGGCGACCACCGAGATCTACACTCTTTCCCTACACGACGCTCTTCCGATCT
Illumina Paired End PCR Primer 2 CAAGCAGAAGACGGCATACGAGATCGGTCTCGGCATTCCTGCTGAACCGCTCTTCCGATCT
Illumina Paried End Sequencing Primer 1 ACACTCTTTCCCTACACGACGCTCTTCCGATCT
Illumina Paired End Sequencing Primer 2 CGGTCTCGGCATTCCTACTGAACCGCTCTTCCGATCT
Illumina DpnII expression Adapter 1 ACAGGTTCAGAGTTCTACAGTCCGAC
Illumina DpnII expression Adapter 2 CAAGCAGAAGACGGCATACGA
Illumina DpnII expression PCR Primer 1 CAAGCAGAAGACGGCATACGA
Illumina DpnII expression PCR Primer 2 AATGATACGGCGACCACCGACAGGTTCAGAGTTCTACAGTCCGA
Illumina DpnII expression Sequencing Primer CGACAGGTTCAGAGTTCTACAGTCCGACGATC
Illumina NlaIII expression Adapter 1 ACAGGTTCAGAGTTCTACAGTCCGACATG
Illumina NlaIII expression Adapter 2 CAAGCAGAAGACGGCATACGA
Illumina NlaIII expression PCR Primer 1 CAAGCAGAAGACGGCATACGA
Illumina NlaIII expression PCR Primer 2 AATGATACGGCGACCACCGACAGGTTCAGAGTTCTACAGTCCGA
Illumina NlaIII expression Sequencing Primer CCGACAGGTTCAGAGTTCTACAGTCCGACATG
Illumina Small RNA Adapter 1 GTTCAGAGTTCTACAGTCCGACGATC
Illumina Small RNA Adapter 2 TCGTATGCCGTCTTCTGCTTGT
Illumina Small RNA RT Primer CAAGCAGAAGACGGCATACGA
Illumina Small RNA PCR Primer 1 CAAGCAGAAGACGGCATACGA
Illumina Small RNA PCR Primer 2 AATGATACGGCGACCACCGACAGGTTCAGAGTTCTACAGTCCGA
Illumina Small RNA Sequencing Primer CGACAGGTTCAGAGTTCTACAGTCCGACGATC
Illumina Multiplexing Adapter 1 GATCGGAAGAGCACACGTCT
Illumina Multiplexing Adapter 2 ACACTCTTTCCCTACACGACGCTCTTCCGATCT
Illumina Multiplexing PCR Primer 1.01 AATGATACGGCGACCACCGAGATCTACACTCTTTCCCTACACGACGCTCTTCCGATCT
Illumina Multiplexing PCR Primer 2.01 GTGACTGGAGTTCAGACGTGTGCTCTTCCGATCT
Illumina Multiplexing Read1 Sequencing Primer ACACTCTTTCCCTACACGACGCTCTTCCGATCT
Illumina Multiplexing Index Sequencing Primer GATCGGAAGAGCACACGTCTGAACTCCAGTCAC
Illumina Multiplexing Read2 Sequencing Primer GTGACTGGAGTTCAGACGTGTGCTCTTCCGATCT
Illumina PCR Primer Index 1 CAAGCAGAAGACGGCATACGAGATCGTGATGTGACTGGAGTTC
Illumina PCR Primer Index 2 CAAGCAGAAGACGGCATACGAGATACATCGGTGACTGGAGTTC
Illumina PCR Primer Index 3 CAAGCAGAAGACGGCATACGAGATGCCTAAGTGACTGGAGTTC
Illumina PCR Primer Index 4 CAAGCAGAAGACGGCATACGAGATTGGTCAGTGACTGGAGTTC
Illumina PCR Primer Index 5 CAAGCAGAAGACGGCATACGAGATCACTGTGTGACTGGAGTTC
Illumina PCR Primer Index 6 CAAGCAGAAGACGGCATACGAGATATTGGCGTGACTGGAGTTC
Illumina PCR Primer Index 7 CAAGCAGAAGACGGCATACGAGATGATCTGGTGACTGGAGTTC
Illumina PCR Primer Index 8 CAAGCAGAAGACGGCATACGAGATTCAAGTGTGACTGGAGTTC
Illumina PCR Primer Index 9 CAAGCAGAAGACGGCATACGAGATCTGATCGTGACTGGAGTTC
Illumina PCR Primer Index 10 CAAGCAGAAGACGGCATACGAGATAAGCTAGTGACTGGAGTTC
Illumina PCR Primer Index 11 CAAGCAGAAGACGGCATACGAGATGTAGCCGTGACTGGAGTTC
Illumina PCR Primer Index 12 CAAGCAGAAGACGGCATACGAGATTACAAGGTGACTGGAGTTC
Illumina DpnII Gex Adapter 1 GATCGTCGGACTGTAGAACTCTGAAC
Illumina DpnII Gex Adapter 1.01 ACAGGTTCAGAGTTCTACAGTCCGAC
Illumina DpnII Gex Adapter 2 CAAGCAGAAGACGGCATACGA
Illumina DpnII Gex Adapter 2.01 TCGTATGCCGTCTTCTGCTTG
Illumina DpnII Gex PCR Primer 1 CAAGCAGAAGACGGCATACGA
Illumina DpnII Gex PCR Primer 2 AATGATACGGCGACCACCGACAGGTTCAGAGTTCTACAGTCCGA
Illumina DpnII Gex Sequencing Primer CGACAGGTTCAGAGTTCTACAGTCCGACGATC
Illumina NlaIII Gex Adapter 1.01 TCGGACTGTAGAACTCTGAAC
Illumina NlaIII Gex Adapter 1.02 ACAGGTTCAGAGTTCTACAGTCCGACATG
Illumina NlaIII Gex Adapter 2.01 CAAGCAGAAGACGGCATACGA
Illumina NlaIII Gex Adapter 2.02 TCGTATGCCGTCTTCTGCTTG
Illumina NlaIII Gex PCR Primer 1 CAAGCAGAAGACGGCATACGA
Illumina NlaIII Gex PCR Primer 2 AATGATACGGCGACCACCGACAGGTTCAGAGTTCTACAGTCCGA
Illumina NlaIII Gex Sequencing Primer CCGACAGGTTCAGAGTTCTACAGTCCGACATG
Illumina Small RNA RT Primer CAAGCAGAAGACGGCATACGA
Illumina 5p RNA Adapter GTTCAGAGTTCTACAGTCCGACGATC
Illumina RNA Adapter1 TCGTATGCCGTCTTCTGCTTGT
Illumina Small RNA 3p Adapter 1 ATCTCGTATGCCGTCTTCTGCTTG
Illumina Small RNA PCR Primer 1 CAAGCAGAAGACGGCATACGA
Illumina Small RNA PCR Primer 2 AATGATACGGCGACCACCGACAGGTTCAGAGTTCTACAGTCCGA
Illumina Small RNA Sequencing Primer CGACAGGTTCAGAGTTCTACAGTCCGACGATC
TruSeq Universal Adapter AATGATACGGCGACCACCGAGATCTACACTCTTTCCCTACACGACGCTCTTCCGATCT
TruSeq Adapter, Index 1 GATCGGAAGAGCACACGTCTGAACTCCAGTCACATCACGATCTCGTATGCCGTCTTCTGCTTG
TruSeq Adapter, Index 2 GATCGGAAGAGCACACGTCTGAACTCCAGTCACCGATGTATCTCGTATGCCGTCTTCTGCTTG
TruSeq Adapter, Index 3 GATCGGAAGAGCACACGTCTGAACTCCAGTCACTTAGGCATCTCGTATGCCGTCTTCTGCTTG
TruSeq Adapter, Index 4 GATCGGAAGAGCACACGTCTGAACTCCAGTCACTGACCAATCTCGTATGCCGTCTTCTGCTTG
TruSeq Adapter, Index 5 GATCGGAAGAGCACACGTCTGAACTCCAGTCACACAGTGATCTCGTATGCCGTCTTCTGCTTG
TruSeq Adapter, Index 6 GATCGGAAGAGCACACGTCTGAACTCCAGTCACGCCAATATCTCGTATGCCGTCTTCTGCTTG
TruSeq Adapter, Index 7 GATCGGAAGAGCACACGTCTGAACTCCAGTCACCAGATCATCTCGTATGCCGTCTTCTGCTTG
TruSeq Adapter, Index 8 GATCGGAAGAGCACACGTCTGAACTCCAGTCACACTTGAATCTCGTATGCCGTCTTCTGCTTG
TruSeq Adapter, Index 9 GATCGGAAGAGCACACGTCTGAACTCCAGTCACGATCAGATCTCGTATGCCGTCTTCTGCTTG
TruSeq Adapter, Index 10 GATCGGAAGAGCACACGTCTGAACTCCAGTCACTAGCTTATCTCGTATGCCGTCTTCTGCTTG
TruSeq Adapter, Index 11 GATCGGAAGAGCACACGTCTGAACTCCAGTCACGGCTACATCTCGTATGCCGTCTTCTGCTTG
TruSeq Adapter, Index 12 GATCGGAAGAGCACACGTCTGAACTCCAGTCACCTTGTAATCTCGTATGCCGTCTTCTGCTTG
Illumina RNA RT Primer GCCTTGGCACCCGAGAATTCCA
Illumina RNA PCR Primer AATGATACGGCGACCACCGAGATCTACACGTTCAGAGTTCTACAGTCCGA
RNA PCR Primer, Index 1 CAAGCAGAAGACGGCATACGAGATCGTGATGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 2 CAAGCAGAAGACGGCATACGAGATACATCGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 3 CAAGCAGAAGACGGCATACGAGATGCCTAAGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 4 CAAGCAGAAGACGGCATACGAGATTGGTCAGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 5 CAAGCAGAAGACGGCATACGAGATCACTGTGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 6 CAAGCAGAAGACGGCATACGAGATATTGGCGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 7 CAAGCAGAAGACGGCATACGAGATGATCTGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 8 CAAGCAGAAGACGGCATACGAGATTCAAGTGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 9 CAAGCAGAAGACGGCATACGAGATCTGATCGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 10 CAAGCAGAAGACGGCATACGAGATAAGCTAGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 11 CAAGCAGAAGACGGCATACGAGATGTAGCCGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 12 CAAGCAGAAGACGGCATACGAGATTACAAGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 13 CAAGCAGAAGACGGCATACGAGATTTGACTGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 14 CAAGCAGAAGACGGCATACGAGATGGAACTGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 15 CAAGCAGAAGACGGCATACGAGATTGACATGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 16 CAAGCAGAAGACGGCATACGAGATGGACGGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 17 CAAGCAGAAGACGGCATACGAGATCTCTACGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 18 CAAGCAGAAGACGGCATACGAGATGCGGACGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 19 CAAGCAGAAGACGGCATACGAGATTTTCACGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 20 CAAGCAGAAGACGGCATACGAGATGGCCACGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 21 CAAGCAGAAGACGGCATACGAGATCGAAACGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 22 CAAGCAGAAGACGGCATACGAGATCGTACGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 23 CAAGCAGAAGACGGCATACGAGATCCACTCGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 24 CAAGCAGAAGACGGCATACGAGATGCTACCGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 25 CAAGCAGAAGACGGCATACGAGATATCAGTGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 26 CAAGCAGAAGACGGCATACGAGATGCTCATGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 27 CAAGCAGAAGACGGCATACGAGATAGGAATGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 28 CAAGCAGAAGACGGCATACGAGATCTTTTGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 29 CAAGCAGAAGACGGCATACGAGATTAGTTGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 30 CAAGCAGAAGACGGCATACGAGATCCGGTGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 31 CAAGCAGAAGACGGCATACGAGATATCGTGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 32 CAAGCAGAAGACGGCATACGAGATTGAGTGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 33 CAAGCAGAAGACGGCATACGAGATCGCCTGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 34 CAAGCAGAAGACGGCATACGAGATGCCATGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 35 CAAGCAGAAGACGGCATACGAGATAAAATGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 36 CAAGCAGAAGACGGCATACGAGATTGTTGGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 37 CAAGCAGAAGACGGCATACGAGATATTCCGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 38 CAAGCAGAAGACGGCATACGAGATAGCTAGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 39 CAAGCAGAAGACGGCATACGAGATGTATAGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 40 CAAGCAGAAGACGGCATACGAGATTCTGAGGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 41 CAAGCAGAAGACGGCATACGAGATGTCGTCGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 42 CAAGCAGAAGACGGCATACGAGATCGATTAGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 43 CAAGCAGAAGACGGCATACGAGATGCTGTAGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 44 CAAGCAGAAGACGGCATACGAGATATTATAGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 45 CAAGCAGAAGACGGCATACGAGATGAATGAGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 46 CAAGCAGAAGACGGCATACGAGATTCGGGAGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 47 CAAGCAGAAGACGGCATACGAGATCTTCGAGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
RNA PCR Primer, Index 48 CAAGCAGAAGACGGCATACGAGATTGCCGAGTGACTGGAGTTCCTTGGCACCCGAGAATTCCA
ABI Dynabead EcoP Oligo CTGATCTAGAGGTACCGGATCCCAGCAGT
ABI Solid3 Adapter A CTGCCCCGGGTTCCTCATTCTCTCAGCAGCATG
ABI Solid3 Adapter B CCACTACGCCTCCGCTTTCCTCTCTATGGGCAGTCGGTGAT
ABI Solid3 5' AMP Primer CCACTACGCCTCCGCTTTCCTCTCTATG
ABI Solid3 3' AMP Primer CTGCCCCGGGTTCCTCATTCT
ABI Solid3 EF1 alpha Sense Primer CATGTGTGTTGAGAGCTTC
ABI Solid3 EF1 alpha Antisense Primer GAAAACCAAAGTGGTCCAC
ABI Solid3 GAPDH Forward Primer TTAGCACCCCTGGCCAAGG
ABI Solid3 GAPDH Reverse Primer CTTACTCCTTGGAGGCCATG