In such situations, I find it best to use named parameters to explicitely choose which is being passed:

sub doFile {
    my (%param) = @_;

    if ( defined($param{'filename'}) ) {
        warn( "We were passed a filename.\n" );
    }
    elsif ( defined($param{'filehandle'}) ) {
        warn( "We were passed a filehandle.\n" );
    }
    else {
        die( "We did not get a filename or filehandle.\n" );
    }
}

# this for a filename:
doFile( filename => 'foobar.qux' );

# or this for a filehandle:
doFile( filehandle => \*DATA ); # or filehandle => $fh
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