if I do it thru a reference the content will change in the next loop when I modify @currentFile again

Don't define @currentfile in that scope then.

my @combinedData;
my @filesList = <*>;

foreach my $file (@filesList) {
   my @currentFile;
   open(F, "file.txt") or die("Unable to open file");
   @currentFile = <F>;

   # HOW TO COMBINE IT INTO @combinedData ?
   push @combinedData, \@currentFile;
}
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