Try the following instructions.
1. Backup the default Barcode Labels report here (copy-paste corresponding folder):
c:\Users\%username%\AppData\Local\eMagicOne Store Manager for PrestaShop\Custom_Reports\
2. In Store Manager go to Reports -> Custom Reports -> Edit "Barcode Labels" report
3. Click "Design Report" button
4. Click on "MasterData1" label and press Ctrl+C (copy)
5. Press Ctrl+V (paste) for a few times (6 per one A4 page)
6. Save the report design
7. Go to products grid and select the "newcomming" product that you want to print labels for (you may select multiple products)
8. Right-click on the selected products and go to Reports -> Barcode Labels
This will print multiple barcode labels for selected products.
This is not exactly what you described - you can not control how many labels will be printed per product by "newcomming" quantity.
However, you can specify exactly what products you want to print labels for and you can print them in bulk, discarding extra labels or saving them for future.