Some ssDNA products may have strong aggregation tendency due to the nature of their nucleotide sequences. These aggregates are most likely formed due to intramolecular and/or intermolecular forces.
To test whether the extra band in a gel image is ssDNA aggregates or dsDNA contamination, you can perform a digestion test using S1 Nuclease, which degrades ssDNA, but not dsDNA. If the ssDNA product is 100% pure, with no dsDNA, then all samples should be digested with S1 Nuclease and no band should be observed after running gel electrophoresis. However, if a product has dsDNA contamination, then it can’t be fully digested after the addition of S1 Nuclease and still have bands present on the gel image.
To further confirm whether the extra band is indeed ssDNA aggregates, you can cut out the ssDNA band on the gel and run a second around of gel electrophoresis. If the extra band is aggregated ssDNA molecules, it will still show up on the second gel after purification. In addition, the ratio of the extra band over the ssDNA band in the two gels would remain similar.