"During variant calling bcftools compares the average mapping quality of reads supporting a variant with those they don't. If there is a significant difference it will skip this variant. " Are there someone that can explain me how to create a BAM file with the reads that didn't supported the variant calling process in this case?
Can you provide the source of the statement?
Anyway, not a direct answer but you can negate this filtering by just filtering out all reads below a certain MAPQ threshold, e.g., MAPQ 60:
samtools view -bq 60 Aligned.bam > Aligned_FiltMAPQ.bam
Then, there cannot be a statistically significant difference (based on MAPQ) between those reads that support a call versus those that don't.