use Modern::Perl;

my %hash;

do {chomp; $_ = qq|$_"$hash{$1}"| if /(ID=.+)$/ and ++$hash{$1}; say}
  for <DATA>;

__DATA__
xxxx . yyy 521 916 . + . ID=OSCAR1028v1rpkm9.67

xxxx . xxx 521 567 . + . Parent=OSCAR1028v1rpkm9.67

xxxx . yyy 126 130 . - . ID=OSCAR10281vrpkm9.67

xxxx . xxx 129 130 . - . Parent=OSCAR1028v1rpkm9.67

xxxx . yyy 126 130 . - . ID=OSCAR10281vrpkm9.67

xxxx . xxx 129 130 . - . Parent=OSCAR1028v1rpkm9.67