for f in /completepath/*
do
    [ -d $f ] && cd "$f" && echo Entering into $f
    for y in `ls *.fastq.gz | sed 's/_L00[1234]_R1_001.fastq.gz//g' | sort -u`
    do
        echo ${y}
    done
done

Entering into /completepath/m_i_cast_avpv_1
iavpvcast1_S6
Entering into /completepath/m_i_cast_avpv_2
iavpvcast2_S6
Entering into /completepath/m_i_int_avpv_1
iavpvint1_S5
Entering into /completepath/m_i_int_avpv_2
iavpvint2_S5
Entering into /completepath/m_p_cast_avpv_1
pavpvcast1_S8
Entering into /completepathd/m_p_int_avpv_1
pavpvint1_S7
Entering into /completepath/m_p_int_avpv_2
pavpvint2_S7
pavpvint2_S7
pavpvint2_S7
pavpvint2_S7