You have done whole genome sequencing of the ancient DNA and have re-aligned it to the current reference genome?, and you notice many regions where there was alignment (or low alignment coverage) due to having none-to-little input DNA template?

I would see this as a de novo assembly opportunity and aim to assemble the reads you've got, which will allow you to produce a consensus set of contigs that may have gaps (Ns). You could then re-align your sample to the new new genome and call variants over it.

You could also mess around with these (or other scripts) that will easily allow you to see which regions in your BAM are at 0 or low coverage:

#Determine number of bases at 0 read depth
zero=$(bedtools genomecov -ibam BAM -g hg38.fasta -bga | awk '$4==0 {bpCountZero+=($3-$2)} {print bpCountZero}' | tail -1)

#Determine number of bases at >0 read depth, i.e., non-zero bases
nonzero=$(bedtools genomecov -ibam BAM -g hg38.fasta -bga | awk '$4>0 {bpCountNonZero+=($3-$2)} {print bpCountNonZero}' | tail -1)

#Calculate the percent of the reference genome covered by >0 read depth bases
#Round up to 6 decimal places
percent=$(bc <<< "scale=6; ($nonzero / ($zero + $nonzero))*100")

echo $percent

.

#Output all bases in the reference genome at >=3 read depth
bedtools genomecov -ibam BAM -g hg38.fasta -bga | awk '$4>2'