Drop out of single quotes:

for i in 1 2 3 4 5 6 7 10 11 12 ; do
  perl -lane'print "p'$i'\t$_"' p$i.chr7.miRNA.txt
done
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Or use double quotes: (Don't forget to escape what needs to be escaped.)

for i in 1 2 3 4 5 6 7 10 11 12 ; do
  perl -lane"print qq{p$i\\t\$_}" p$i.chr7.miRNA.txt
done
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Or pass it as an argument:

for i in 1 2 3 4 5 6 7 10 11 12 ; do
  perl -lane'BEGIN { $i = shift(@ARGV); }
    print "p$i\t$_"' $i p$i.chr7.miRNA.txt
done
[download]